Now You Try

<p>Where appropriate, sketch all possible triangles, given each set of information. Label all side lengths to the nearest tenth of a centimetre and all angles to the nearest degree.</p><p><code class='latex inline'>
\displaystyle
a = 1.3 cm, b = 2.8 cm, \angle A = 33^o
</code></p>

<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>\angle A</code> is <code class='latex inline'>40^o</code>, <code class='latex inline'>a = 10 cm</code>, and <code class='latex inline'>b =12 cm</code>. Determine <code class='latex inline'>c</code>, to the nearest tenth of a centimetre?</p><p>(a) Determine if this is a ambiguous case.</p><p>(b) Solve for side <code class='latex inline'>c</code> in both triangles. How many valid solutions are there?</p>

<p>At the end of a dock, high tide of 16m is recorded at 9:00 am. Low tide of 6 m is recorded at 3:00 pm. A sinusoidal function can model the water depth versus time.</p><p>a) Construct a model for the water depth using a cosine function, where time is measured in hours past high tide.</p><p>b) Construct a model for the water depth using a sine function, where time is measured in hours past high tide.</p><p>c) Construct a model for the water depth using a sine function, where time is measured in hours past low tide.</p><p>d) Construct a model for the water depth using a cosine function, where time is measured in hours past
low tide.</p><p>e) Compare your models. Which is the simplest representation if time is referenced to high tide? low tide? Explain why there is a difference.</p>

<p>Where appropriate, sketch all possible triangles, given each set of information. Label all side lengths to the nearest tenth of a centimetre and all angles to the nearest degree.</p><p><code class='latex inline'>
\displaystyle
a = 7.3 \text{ m}, b = 14.6 \text{ m}, \angle A = 30^{\circ}
</code></p>

<p>Transform the graph of <code class='latex inline'>f(x) = cos x</code> to <code class='latex inline'>g(x) = \dfrac{3}{4} cos[6(x + 45^{\circ})] - 2</code>. Show
each step in the transformation.</p>

<p>Write an equation in the form <code class='latex inline'>y = a sin [k(x - d)] + c</code> that represents the graph of <code class='latex inline'>y = sin x</code> after it is reflected in the x-axis, vertically stretched by a factor of 3, horizontally compressed by a factor of shifted <code class='latex inline'>35^{\circ}</code> to the left, and translated 8 units down.</p>

<p>Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.</p><p><code class='latex inline'>a = 11.1 cm, c = 5.2 cm, \angle C = 33^{\circ}</code></p>

<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>\angle A</code> is <code class='latex inline'>40^o</code>, <code class='latex inline'>a = 10 cm</code>, and <code class='latex inline'>b =12 cm</code>. Determine <code class='latex inline'>c</code>, to the nearest tenth of a centimetre?</p><p>(a) If side a is 7 cm rather than 10 cm, how many solutions are there? Explain why.</p><p>(b) Determine the minimum value of a that results in at least one solutions. Calculate your answer to four decimal places.</p>

<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>\angle A</code> is <code class='latex inline'>40^o</code>, <code class='latex inline'>a = 10 cm</code>, and <code class='latex inline'>b =12 cm</code>. Determine <code class='latex inline'>c</code>, to the nearest tenth of a centimetre?</p><p>If side a is 12 cm rather than 10 cm, how many solutions are there? Explain why.</p>

<p>Where appropriate, sketch all possible triangles, given each set of information. Label all side lengths to the nearest tenth of a centimetre and all angles to the nearest degree.</p><p><code class='latex inline'>
\displaystyle
a = 7.2 mm, b = 9.3 mm, \angle A = 35^o
</code></p>

<p>Given each set of information. determine how many triangles can be drawn. Calculate, then label, all side lengths to the nearest tenth and all interior angles to the nearest degree, where appropriate.</p><p><code class='latex inline'>a = 2.1 cm, b = 6.1 cm</code>, and <code class='latex inline'>\angle A = 20^o</code>.</p>

<p>Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.</p><p><code class='latex inline'>b = 12.1 cm, c = 8.2 cm, \angle C = 34^{\circ}</code></p>

<p>Given each set of information. determine how many triangles can be drawn. Calculate, then label, all side lengths to the nearest tenth and all interior angles to the nearest degree, where appropriate.</p><p><code class='latex inline'>a = 1.5 cm, b =2.8 cm</code>, and <code class='latex inline'>\angle A = 41^o</code>.</p>

<p>Two forest fire stations, P and Q, are 20.0 km apart. A ranger at station Q sees a fire 15.0 km away. If the angle between the line PQ and the line from P to the fire is <code class='latex inline'>25^{\circ}</code>, how far, to the nearest tenth of a kilometre, is station P from the fire?</p>

<p>Determine the equation of a sine function that represents the graph shown.</p><img src="/qimages/23282" />

<p>Determine whether it is possible to draw a triangle given each set of information. Sketch all possible triangles where appropriate. Calculate, then label, all side lengths to the nearest tenth of ta centimetre and all angles to the nearest degree.</p><p><code class='latex inline'>b = 3.0 cm, c = 5.5 cm, \angle B = 30^{\circ}</code></p>

<p>Transform the graph of <code class='latex inline'>f(x) = sin x</code> to <code class='latex inline'>g(x) = -3 sin[\dfrac{1}{4}(x - 50^{\circ})] + 7</code>. Show each step in the transformation.</p>

<p> In <code class='latex inline'>\triangle ABC</code>, find area of triangle if <code class='latex inline'>\angle BAC = 30^{\circ}</code> and <code class='latex inline'>AB = 20</code> and <code class='latex inline'>BC = 12</code>.</p>