Download Geometry Lesson 7-6: Apply Trigonometric Ratios to find Missing

Geometry Lesson 7-6: Apply Trigonometric Ratios to find Missing Angles
Learning Target: By the end of today’s lesson we will be able to successfully use the sine, cosine, and tangent
ratios for indirect measurement.
Previously, we have used trigonometric ratios to find the missing side lengths in right triangles. Using these
same ratios, we can determine the angle measures in right triangles, if we are given two side lengths.
Example 1: Use the trig ratio cos A =
Example 2: Use the trig ratio sin A =
24
to determine which angle is A.
25
8
to determine which angle is A.
17
In the previous lesson we learned that sin 30° =________. Conversely, if you know that the sine of an acute
angle is __________, you can conclude that the angle measures 30°.
Example 3: Use your calculator to find each angle measure to the nearest degree.
a.) cos –1(0.87)
b.) sin–1 (0.85)
c.) tan–1 (0.71)
Example 4: Find the unknown measures. Round each angle measure to the nearest degree.
a.) R
b.) A
Example 5: A ladder leans against a building. The foot of the ladder is 6 feet from the building and the ladder
reaches a height of 14 feet on the building. To the nearest degree, find the angle that the ladder
makes with the ground.
Example 6: You are building a track for a model train. You want the track to incline from the first level to the
level, 4 inches higher, in 96 inches. Is the angle of elevation less than 3°?
Example 7: A piece of lumber leans against a wall. The top of this 40 foot piece of lumber touches a point on
the wall that is 36 feel above the ground. To the nearest degree, find the measure of the angle that
the lumber makes with the wall.
Example 8: A highway sign warns that a section of road ahead has a 7% grade. To the nearest degree what
7
angle does the road make with a horizontal line? (Hint: 7% =
)
100
Example 9: Baldwin St. in Dunedin, New Zealand, is the steepest street in the world. It has a grade of 38%.
To the nearest degree, what angles does Baldwin St. make with a horizontal line?