Download 8.1 Right Triangle Trig

Precalculus 8.1 Right Triangle Trigonometry; Applications
Objective: able to find the exact value of trigonometric functions of acute angles using right triangles; use complementary
angle theorem; solve right triangles; solve applied problems
Express the six trigonometric functions of an acute angel of a right triangle as the ratio of the sides of the
right triangle.
Theorem:
Cofunctions of complementary angles are equal
1. Find the exact value of tan 12˚ – cot 78˚ without using a calculator.
m∠B = 20° , and b = 5, solve the triangle. Round
2. Given a right triangle ABC with m∠C = 90° ,
angle measures to the nearest tenth and side lengths to the nearest hundredths.
3. Given a right triangle ABC with m∠C = 90° , a = 2, and b = 8, solve the triangle. Round angle
measures to the nearest tenth and side lengths to the nearest hundredths.
What are angle of elevation and angle of depression?
4. A ship, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff.
The angle of elevation is found to be 25˚. How far offshore is the ship?
In navigation and surveying, the direction or bearing from a point O to a point P equals the acute angle
between the ray OP and the vertical line through O, the north-south line.
5. A ship leaves the port of Miami with a bearing of S80˚E and a speed of 15 knots. After 1 hour, the ship
turns 90˚ toward the south. After 2 hours, maintaining the same speed, what is the bearing to the ship from
port?
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