Homework

Problem 1 · easy

A right triangle has legs 5 and 12. Find all six trig ratios for the angle opposite the side of length 5.

Problem 2 · easy

Find sin(45°) without a calculator.

Problem 3 · easy

Find tan(60°) without a calculator.

Problem 4 · easy

Find cos(30°) without a calculator.

Problem 5 · easy

If sin(θ) = 5/13 and θ is in Quadrant I, find cos(θ).

Problem 6 · medium

If cos(θ) = -3/5 and θ is in Quadrant II, find sin(θ).

Problem 7 · medium

Find tan(θ) if sin(θ) = 2/sqrt(5) and θ is in Quadrant I.

Problem 8 · easy

Find the reference angle for θ = 135°.

Problem 9 · easy

Find the reference angle for θ = 240°.

Problem 10 · medium

Find sin(150°) using reference angles.

Problem 11 · medium

Find cos(210°) using reference angles.

Problem 12 · medium

Find tan(315°) using reference angles.

Problem 13 · medium

Solve the right triangle: angle A=50°, hypotenuse=10. Find side a (opposite A) and side b.

Problem 14 · medium

Solve the right triangle: legs a=7 and b=24. Find the hypotenuse and angle A.

Problem 15 · medium

A building casts a 40 ft shadow when the sun is at 35° elevation. Find the building's height.

Problem 16 · medium

From the top of a 100 ft cliff, you see a boat at a 25° angle of depression. How far is the boat from the base of the cliff?

Problem 17 · easy

Find csc(30°) without a calculator.

Problem 18 · easy

Find sec(45°) without a calculator.

Problem 19 · challenge

If tan(θ) = -4/3 and θ is in Quadrant IV, find sin(θ) and cos(θ).

Problem 20 · medium

Find all six trig functions for 30° from memory.

Problem 21 · medium

A ladder 15 ft long leans against a wall at 65°. How high up the wall does it reach?

Problem 22 · medium

Find sin(270°).

Problem 23 · challenge

Use a Pythagorean identity to find sec(θ) if tan(θ) = 2 and θ is in Quadrant III.

Problem 24 · challenge

Two observers on opposite ends of a valley, 1 km apart, both sight the top of a mountain. Observer A sees it at 42° elevation, B at 57°. Set up (do not solve) the system to find the mountain's height.

Problem 25 · easy

A 30-60-90 triangle has hypotenuse 10. Find both legs.