Determine the indicated side lengths in the triangles.

Two trees cast a shadow when the Sun is up. The shadow of one tree is 12.1 m long. The shadow of the other tree is 7.6 m long. If the shorter tree is 5.8 m tall, determine the height of the taller tree. Round your answer to the nearest tenth of a metre.

Determine each unknown value. Round your answer to one decimal place.

a) \sin 28^o = \frac{x}{5}

b) \cos 43^o = \frac{13}{y}

c) \tan A = 7.1154

d) \cos B = \frac{7}{9}

Determine the length of the indicated side or the measure of the indicated angle.

Determine the length of the indicated side or the measure of the indicated angle.

Solve the triangle

In \triangle ABC, \angle A = 90^o, \angle B = 14^o, and b = 5.3 cm.

Solve the triangle

In \triangle DEF, \angle F = 90^o, d = 7.8 mm, and e = 6.9 mm.

A ramp has an angle of elevation of 4.8° and a rise of 1.20 m, as shown at the left. How long is the ramp and what is its run? Round your answers to the nearest hundredth of a metre.

Surveyors need to determine the width of a river. Explain how they can do this without crossing the river. Use a diagram to illustrate your answer.

Jane is on the fifth floor of an office building 16 m above the ground. She spots her car and estimates that it is parked 20 m from the base of the building. Determine the angle of depression to the nearest degree.

A pilot who is heading due north spots two forest fires. The fire that is due east is at an angle of depression of 47°. The fire that is due west is at an angle of depression of 38°. What is the distance between the two fires, to the nearest metre, if the altitude of the airplane is 2400 m?