A spotlight on a 3.0 m Stand shines on the surface of a swimming pool. The beam of light hits the water at a point 7.0 m away from the base of the stand.

a) Calculate the angle the beam makes with the pool surface. Round your answer to the nearest degree.

b) The beam reflects off the pool surface and strikes a wall 4.5 m away from the reflection point. The angle the beam makes with the pool is exactly the same on either side ofrhe reflection point. Calculate how far up the wall, to the nearest tenth of a metre, the spotlight will appear.

The sides of an isosceles triangle are 12 cm. 12 cm, and 16 cm. Use primary trigonometric ratios to determine the largest interior angle to the nearest degree. (Hint: Divide the triangle into two congruent right triangles.)

A coaSt guard boat is tracking two ships using radar. At noon, the ships are 5.0 km apart and the angle between them is 90°. The closest ship is 3.1 km from the coast guard boat. How far, to the nearest tenth of a kilometre, is the Other ship from the coast guard boat?

An overhead Streetlight can illuminate a circular area of diameter 14 m. The light bulb is 6.8 m directly above a bike path. Determine the angle of elevation, to the nearest degree, from the edge of the illuminated area to the light bulb.

Martin’s building is 105 m high. From the roof, he spots his car in the parking lot. He estimates that it is about 70 m from the base of the building.

a) What is the angle of depression, to the nearest degree, from Martin’s eyes to the car?

b) What is the straight—line distance, to the nearest metre, from Martin to his car?

Solve the triangle. Round each length to the nearest unit and each angle to the nearest degree.

\triangle DEF: \angle D = 67^o, \angle F = 42^o, e = 25

From the bottom of a canyon, Rita stands 47 m directly below an overhead bridge. She estimates that the angle of elevation of the bridge is about 35° at the north end and about 40° at the south end. For each question, round your answer to the nearest metre.

a) If the bridge were level, how long would it be?

b) If the bridge were inclined 4° from north to south, how much longer would it be?

The manufacturer of a reclining lawn chair is planning to cut notches on the back of the chair so that you can recline at an angle of 30° as shown.

a) What is the measure of \angle B, to the nearest degree, for the chair to be reclined at the proper angle?

b) Determine the distance from A to B to the nearest centimetre.