4.1 – Right Triangle Trigonometry Objectives: You should be able to find values of trig functions in right triangles and solve right triangles. Vocabulary

Key Concept 1

Example 1: Find the exact values of the six trigonometric functions of θ.

Example 2: If , find the exact values of the five remaining trigonometric functions for the acute angle . Example 2

Key Concept 3

Find a Missing Side Length Example 3: Find the value of x. Round to the nearest tenth, if necessary. Example 3

Example 4: SPORTS A competitor in a hiking competition must climb up the inclined course as shown to reach the finish line. Determine the distance in feet that the competitor must hike to reach the finish line. Example 4

  Example 4

Find a Missing Angle Measure Example 5: Use a trigonometric function to find the measure of θ. Round to the nearest degree, if necessary. Example 5

Angle of Elevation & Angle of Depression What do we know about Angles of Elevation and Depression??? Example 5

Example 6: SKIING The chair lift at a ski resort rises at an angle of 20.75° while traveling up the side of a mountain and attains a vertical height of 1200 feet when it reaches the top. How far does the chair lift travel up the side of the mountain? Example 6

Example 7: AIRPLANE A person on an airplane looks down at a point on the ground at an angle of depression of 15°. The plane is flying at an altitude of 10,000 feet. How far is the person from the point on the ground to the nearest foot? Example 6

Example 8: SIGHTSEEING A sightseer on vacation looks down into a deep canyon using binoculars. The angles of depression to the far bank and near bank of the river below are 61° and 63°, respectively. If the canyon is 1250 feet deep, how wide is the river? Example 7

Example 9: HIKING The angle of elevation from a hiker to the top of a mountain is 25o. After the hiker walks 1000 feet closer to the mountain the angle of elevation is 28o. How tall is the mountain? A. 3791 ft B. 4294 ft C. 7130 ft D. 8970 ft Example 7

Solve a Right Triangle Example 10: Solve ΔFGH. Round side lengths to the nearest tenth and angle measures to the nearest degree. Example 8

Example 11: Find exact value without calc. sin 45º b. cos 30º Exact Values: Hand-Jive Example 11: Find exact value without calc. sin 45º b. cos 30º tan 60º d. sec 60º e. cot 30º f. csc 45º Example 8

  Example 8

Example 13: >, <, or = ? Without calc. sin 45º ____ cot 60º b. tan 45º ____ sec 30º Example 8