Now You Try

<p> Find the tangent of the other acute angle, to four decimal places. </p><img src="/qimages/2375" />

<p>Calculate tan <code class='latex inline'> \mathrm{C} </code> in each triangle.</p><img src="/qimages/65207" />

<p>The shadow of a tree that is 12 m tall measures 9 m in length. Determine the angle of elevation of the sun.</p>

<p>Find the tangent of the angle indicated to four decimal places.</p><img src="/qimages/2370" />

<p>Patricia walked diagonally across a rectangular schoolyard measuring 45 m by 65 In. To the nearest degree, at what angle with respect to the shorter side did she walk?</p>

<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre.</p><img src="/qimages/2388" />

<p>Find the length of the unknown side, to the nearest tenth.</p><img src="/qimages/2382" />

<p>The diagram shows the roof of a house. How wide is the house, to the nearest metres?</p><img src="/qimages/6482" />

<p>Evaluate with a calculator. Record your answer to four decimal places. </p><p><code class='latex inline'>
\displaystyle
\begin{array}{ccccccc}
& a)& \tan65^\circ & b) &\tan15^\circ & c) & \tan62^\circ & d) & \tan30.7^\circ \\
& e)& \tan82.4^\circ & f)& \tan82.4^\circ & g) & \tan20.5^\circ & h) & \tan45^\circ \\
\end{array}
</code></p>

<p> Find the tangent of the other acute angle, to four decimal places. </p><img src="/qimages/2371" />

<p>Find the length of the unknown side, to the nearest tenth.</p><img src="/qimages/2381" />

<p>The angle <code class='latex inline'>\theta</code> at which a skier slides down a hill with a coefficient of friction, <code class='latex inline'>u</code>, at a constant speed, is given by <code class='latex inline'>\tan \theta = \mu</code>. Natalie is skiing on a hill with a reported coefficient of friction of <code class='latex inline'>0.6</code>. If Natalie skis down at a constant speed, what is the angle of the hill?</p>

<p>Calculate tan <code class='latex inline'> \mathrm{C} </code> in each triangle.</p><img src="/qimages/65208" />

<p>Find the tangent of the angle indicated to four decimal places.</p><img src="/qimages/2374" />

<p>Police headquarters and the trouble site are shown below.</p><img src="/qimages/6482" /><p>Squad cars and a helicopter are both immediately dispatched to the site from headquarters. </p><p>a) At what angle to Chestnut Street should the helicopter travel?</p><p>b) Assuming that the squad cars can travel at an average speed of 60 km/h and the helicopter can travel twice as fast, how much longe3r will it take for the squad cars to reach the site than the helicopters?</p><p>c) Describe any assumptions you make in your solutions.</p>

<p>Find the length of the unknown side, to the nearest tenth.</p><img src="/qimages/156253" />

<p>The graph of the line <code class='latex inline'> y=x+2 </code> is shown.</p><p>b) Find the measure of the acute angle that the line <code class='latex inline'> y=x-3 </code>
makes with the <code class='latex inline'> x </code> -axis.</p><img src="/qimages/65251" />

<p>Find the tangent of the angle indicated to four decimal places.</p><img src="/qimages/2373" />

<p> Find the tangent of the other acute angle, to four decimal places. </p><img src="/qimages/2373" />

<p>The graph of the line <code class='latex inline'> y=x+2 </code> is shown.</p><p>a) Find the measure of the acute angle that the line <code class='latex inline'> y=x+2 </code>
makes with the <code class='latex inline'> x </code> -axis.</p><img src="/qimages/65247" />

<p>At hockey practice, Lars has the puck in front of the net, as shown.</p><img src="/qimages/6486" /><p>He is exactly 8 m away from the middle of the net, which is 2 m wide. Within what angle must Lars fire his shot in order to get it in the net, to the nearest degree?</p>

<p>Find the tangent of the angle indicated to four decimal places.</p><img src="/qimages/2375" />

<p>For each graph,</p><p>i) find the slope of the line</p><p>ii) draw a triangle to find the tangent of the acute angle that the line makes with the x-axis. Find the acute angle. </p><img src="/qimages/6488" />

<p>Find the measures of both acute angles in each triangle, to the nearest degree. </p><img src="/qimages/2376" />

<p>Find the tangent of the angle indicated to four decimal places.</p><img src="/qimages/2371" />

<p>Find the length of <code class='latex inline'>x</code>, then the length of <code class='latex inline'>y</code>, to the nearest tenth of a metre.</p><img src="/qimages/6484" />

<p> Find the tangent of the other acute angle, to four decimal places. </p><img src="/qimages/2370" />

<p>Find the measure of each angle, to the nearest degree. </p><p><code class='latex inline'>
\displaystyle
\begin{array}{ccccccc}
& a)& \tan\theta=1.5 & b) & \tan A=\frac{3}{4} & c) & \tan B=0.6000 & d) & \tan W=\frac{4}{5}\\
& e)& \tan C=0.8333 & f)& \tan\theta=\frac{6}{7} & g) & \tan X=3.0250 & h) & \tan\theta=\frac{15}{9}
\end{array}
</code></p>

<p>Comfortable stairs have a slope of <code class='latex inline'>\frac{3}{4}</code>.</p><p>What angle do the stairs make with the horizontal, to the nearest degree?</p>

<p> Find the tangent of the other acute angle, to four decimal places. </p><img src="/qimages/2372" />

<p>Find the tangent of the angle indicated to four decimal places.</p><img src="/qimages/2372" />

<p>To measure the height of a building, Chico notes that its shadow is 8.5 m long. He also finds that a line joining the top of the building to the tip of the shadow forms a 65° angle with the flat ground.</p><p>a) Draw a diagram to illustrate this situation.</p><p>b) Find the height of the building, to the nearest tenth of a metre.</p>

<p>The graph of the line <code class='latex inline'> y=x+2 </code> is shown.</p><p>c) Find the measure of the acute angle that the line <code class='latex inline'> y=-x+4 </code>
mạkes with the <code class='latex inline'> x </code> -axis.</p><img src="/qimages/65253" />

<p>A surveyor is positioned at a traffic intersection, viewing a marker on the other side of the street. The marker is 19 m from the intersection. The surveyor cannot measure the width directly because there is too much traffic. Find the width of James Street, to the nearest tenth of a metre. </p><img src="/qimages/2391" />

<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a centimetre, then the measure of <code class='latex inline'>\angle y</code>, to the nearest degree.</p><img src="/qimages/6485" />

<p> Find the tangent of the other acute angle, to four decimal places. </p><img src="/qimages/2374" />

<p>Find the measures of both acute angles in each triangle, to the nearest degree. </p><img src="/qimages/2378" />

<p>The tangent ratio is used to design the bank angle for a curved section of roadway.</p><p>Let <code class='latex inline'>\theta</code> be the bank angle required for a speed limit, <code class='latex inline'>V</code>, in kilometres per hour, and a radius, <code class='latex inline'>r</code>, in metres. The angle and the speed limit are related by the formula <code class='latex inline'>\tan \theta = \frac{v^2}{9.8r}</code>. Find the bank angle required for a highway curve of radius 50 m that will carry the traffic moving at 100 km/h.</p>

<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre.</p><img src="/qimages/2389" />

<p>To measure the width of a river, Kristie uses a large rock, and oak tree, and an elm tree, which are positioned as shown.</p><img src="/qimages/2390" /><p>Show how Kristie can use the tangent ratio to find the width of the river, to the nearest metre. </p>

<p>Rocco and Biff are two Koalas sitting at the top of two eucalyptus trees, which are located 10 m apart, as shown. Rocco's tree is exactly half as tall as Biff's tree. From Rocco's point of view, the angle separating Biff and the base of his tree is 70<code class='latex inline'>^\circ</code></p><img src="/qimages/2392" /><p>How high off the ground is each koala?</p>

<p>a) Use a calculator to evaluate the following:</p>
<ul>
<li><code class='latex inline'>\tan 0^o</code></li>
<li><code class='latex inline'>\tan 90^o</code></li>
</ul>
<p>b) Use the definition of the tangent ratio and geometric reasoning to explain your results. Include diagrams in your explanation. </p>

<p>Does Lars have a better chance, a worse chance, or the same chance to score if he positions himself directly in front
of one of the posts, as shown? Explain your reasoning and any assumptions you make.</p><img src="/qimages/6489" />