Download Advanced Geometry LT 6.2: Solve right triangles and application

Advanced Geometry
LT 6.2: Solve right triangles and application problems
using trigonometric ratios
Investigating Trig Ratios
Find each of the following:
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A trigonometric ratio is a ratio of two sides of a right triangle. There are 3 trig ratios, sine, cosine and tangent.
They are defined as follows
Find each of the following. Write each ratio as a fraction and as a decimal rounded to the nearest hundredth.
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What do you notice about the trig ratios from
and
? Why do you think this happens?
Now find the trig ratios for the other acute angles in the triangles.
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What do you notice about these trig ratios compared to the earlier ones?
***Never use the right angle in a trig ratio***
Remembering The Trig Ratios
Finding Trig Ratios of an Acute Angle
Find the trig ratio of each specified angle. Write each ratio as a fraction and as a decimal rounded to the nearest
hundredth.
Finding Sides Using Trig Ratios
Process:
1. Determine which angle you are using
2. Decide which 2 sides you are working with (Opposite, Adjacent, Hypotenuse?)
3. Set up proper trig ratio with a variable for one side length and solve for that variable
Solve for x.
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Finding an Angle Measurement Using Trig Ratios
Process:
1. Determine which angle you are looking for
2. Decide which sides you know (Opposite, Adjacent, Hypotenuse?)
3. Set up proper trig ratio with a variable for the angle and solve for that variable using the inverse trig
ratio
Solve for x.
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13. A student uses the triangle shown to calculate a. Find and explain the student’s error.
14. If you get a question that involves a right triangle, how can you tell whether you should use the Pythagorean
Theorem or a Trigonometric Ratio?
Practice
Solve for each variable.
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Solve each triangle. Round each answer to the nearest tenth. (To solve a triangle means to find all missing parts)
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