Determine whether these triangles are similar. If they are similar, write a proportion statement and determine the scale factor.

State whether the triangles in the diagram are similar. Then determine p.

Calculate the heights of the two ramp supports, x and y. Round your answers to the nearest tenth of a metre.

Brett needs to support a radio tower with guy wires. Each guy wire must run from the top of the tower to its own anchor 9.00 m from the base of the tower. When the tower casts a shadow that is 9.00 m long, Brett’s shadow is 0.60 m long. Brett is 1.85 m tall. What is the length of each guy wire that Brett needs?

a) Determine the three primary trigonometric ratios for \angle A.

b) Calculate the measure of \angle A to the nearest degree.

Determine x to one decimal place.

\displaystyle \tan 46^o = \frac{x}{14.2}

Determine x to one decimal place.

\displaystyle \cos 29^o = \frac{17.3}{x}

ABCD is a rectangle with AB = 15 cm and BC = 10 cm. What is the measure of \angle BAC to the nearest degree?

In \triangle PQR, \angle R = 90^o and p = 12.0 cm.

a) Determine r, when \angle Q = 53^o

b) Determine \angle P, when q = 16.5 cm.

Solve this triangle.

Maria needs to load cars onto a transport truck. She is planning to drive up a ramp, onto the truck bed. The truck bed is 1.5 m high, and the maximum angle of the slope of the ramp is 35°.

a) How far is the rear of the truck from the point where the ramp touches the ground?

b) How long should the ramp be? Round your answer to one decimal place.

A search-and-rescue airplane is flying at an altitude of 1200 m toward a disabled ship. The pilot notes that the angle of depression to the ship is 12^o. How much father does the airplane have to fly to end up directly above the ship?

The angle of elevation from the top of a 16 m building to the top of a second building is 48°. The buildings are 30 m apart. What is the height of the taller building?

A cyclist pedals his bike 6.5 km up a mountain road, which has a steady incline. By the time hehasreachedthetopofthemountain,hehas climbed 1.] km vertically. Calculate the angle ofelevation of the road.

Two watch towers at a historic fort are located 375 m apart. The first tower is 14 m tall, and the second tower is 30 m tall.

a) What is the angle of depression from the top of the second tower to the top of the first tower?

b) The guards in the towers simultaneously spot a suspicious car parked between the towers. The angle of depression from the lower tower to the car is 77°. The angle of depression from the higher tower is 63°. Which guard is closer to the car? Explain how you know.

Calculate the length of AB using the information provided. Show all your steps.

A swimmer observes that from point A, the angle of elevation to the top of a cliff at point D is 30°.

When the swimmer swims toward the cliff for 1.5 min to point B, he estimates that the angle of elevation to the top of the cliff is about 45°.

If the height of the cliff is 70.0 m, calculate the distance the swimmer swam.

A plane takes off in a straight line and travels along this line for 10 s, when it reaches a height of 300 m. If the plane is traveling at 60 m/s, at what angle is the plane ascending?