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Name: _____________________________________________________________
Date: ________________________
Chapter 16: Intro to Trigonometry
Topic 1: Trig Relationships & Triangle Sides
Period: _______
Vocabulary
________________________: The side opposite the right angle in a triangle.
________________________: The side opposite the marked acute angle.
________________________: The side which is one of the rays that form the marked acute angle.
Always label all three sides of a triangle because starting any work on the problem
When labeling the triangle in terms of their LETTERS,
a side is named as the lower case of the angle across
Examples: Label each side as hypotenuse, opposite and adjacent. Letter each side.
1.
2.
TRIGONOMETRY RATIOS
To solve triangle problems for the lengths of sides or values of angles, we use our trig functions.
Based on which sides of the triangle are being used, choose the appropriate ratio.
Name: _____________________________________________________________
Date: ________________________
Period: _______
Examples:
1.
Sin 𝐵 =
2.
Sin 𝐵 =
Cos 𝐵 =
Cos 𝐵 =
Tan 𝐵 =
Tan 𝐵 =
3. Use Pythagorean Theorem to find the third side of the triangle. Then, find the sine, cosine, and tangent
ratios for angle B.
4. Given right triangle ABC, with hypotenuse AB = 8.5 and m<A = 55, find AC and BC to the nearest tenth.
5. In right triangle ABC with the right angle at C, the hypotenuse length AB=15 and measure angle A=35o.
Find leg length BC to the nearest tenth.
6. In triangle JAC, angle A is the right angle. The measure of <J is 50 degrees and the length of the
hypotenuse, JC is 26 meters. Find the measure of sides AC and JA to the nearest tenth of a meter. What is
the measure of the missing angle? Draw a diagram to help you find a solution.
Name: _____________________________________________________________
Date: ________________________
Period: _______
Word Problems
___________________________________________: Angle measured from the ground up. It is always INSIDE the triangle.
___________________________________________: Angle measured from the top of something down. It is always
OUTSIDE the triangle.
When doing word problems, always sketch a picture and label everything that you know
Examples:
1. At a point on the ground 40 meters from the foot of a tree, the angle of elevation of the top of the tree
contains 42 degrees. Find the height of the tree to the nearest meter.
2. A steel cable extends from the top of a building to a point on the ground that is 1000 feet from the base of
the building. At the point where the cable is anchored to the ground, it is determined that the measure of
its angle of elevation is 48 degrees. To the nearest foot, how tall is the building?
3. A ladder is leaning against a house. The foot of the ladder is 6.5 feet from the wall. The ladder makes an
angle of 74 degrees with the level ground. How long is the ladder? Round your answer to the nearest
tenth of a foot.
4. A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing
away from the lamppost is 35o. The distance from the bird to the observer is 25 feet. How tall is the
lamppost to the nearest foot?
Name: _____________________________________________________________
Date: ________________________
Period: _______
5. A forest ranger looking out from the ranger's station can see a forest fire at a 35 degree angle of
depression. The ranger's position is 100 feet above the ground. To the nearest foot, how far is it from
the base of the ranger's station to the fire on level ground with it?
6. From a point 120 meters away from a building, Alexis measures the angle between the ground and the
top of the building and finds that it measures 41o. What is the height of the building? Round your answer
to the nearest meter.
7. The Occupational Safety and Health Administration (OSHA) provides standards for safety at the
workplace. A ladder is leaned against a vertical wall according to OSHA standards and forms an angle of
approximately 75 degrees with the floor.
(a) If the ladder is 25 ft long, what is the distance from the base of the ladder to the base of the wall?
Round your answer to the nearest tenth of a foot.
(b) How high on the wall does the ladder make contact? Round your answer to the nearest tenth.