Solving Right Triangles Using Trigonometric Ratios

10.6a Right Triangle Trig

Finite Math

​

​

​EQ: Thursday, November 30, 2023

• ​How do I use the lengths of the sides of a right triangle to find trig ratios?

• How do I use trig ratios to find missing parts of right triangles?

​Right Triangle Trig

Math Response

Give the sine ratio for θ.

Type answer here

Correct Answer: \frac{3}{5}

Deg^°

Rad

Give the three trig ratios for angle θ.

sin θ =

​Opposite

Hypotenuse

​SOH

Math Response

Give the cosine ratio for θ.

Type answer here

Correct Answer: \frac{4}{5}

Deg^°

Rad

Give the three trig ratios for angle θ.

cos θ =

​Adjacent

Hypotenuse

​CAH

Math Response

Give the tangent ratio for θ.

Type answer here

Correct Answer: \frac{3}{4}

Deg^°

Rad

Give the three trig ratios for angle θ.

tan θ =

​Adjacent

Opposite

​TOA

Multiple Choice

Find the tan θ.

• $$\frac{5}{3}$$

• $$\frac{4}{3}$$

• $$\frac{5}{4}$$

• $$\frac{4}{5}$$

Multiple Choice

Find the tan θ.

• $$\frac{4}{5}$$

• $$\frac{5\sqrt[]{17}}{16}$$

• $$\frac{3}{4}$$

• $$\frac{4}{3}$$

Multiple Choice

Find the cos θ.

• $$\frac{5}{4}$$

• $$\frac{5}{3}$$

• $$\frac{4}{5}$$

• $$\frac{4}{3}$$

Multiple Choice

Find the cos θ.

• $$\frac{3}{5}$$

• $$\frac{5}{3}$$

• $$\frac{4}{5}$$

• $$\frac{4}{3}$$

​Using the Trig Functions on a Calculator

• ​Calculators must be in DEGREES mode!!!

• Trig functions are precise values, use at least 3 decimals, or 4 is better.

Math Response

Give the sin 50^o.

Type answer here

Correct Answer: 0.7660

Deg^°

Rad

Math Response

Give the cos 65^o.

Type answer here

Correct Answer: 0.4226

Deg^°

Rad

Math Response

Give the tan 35^o.

Type answer here

Correct Answer: 0.7002

Deg^°

Rad

Multiple Choice

Find the measure of the side indicated.

• 7.6

• 9.5

• 7.8

• 8.6

h

a

Multiple Choice

Find the missing side.

• 9.1

• 44.1

• 5.0

• 8.0

When the x is in the...


denominator numerator

Multiple Choice

Find the missing side.

• 6.6

• 7.2

• 6.0

• 5.3

Math Response

Find the missing side.

Round the answer to the nearest tenths place.

Type answer here

Correct Answer: 10.1

Deg^°

Rad

Math Response

Find the missing side.

Round the answer to the nearest tenths place.

Type answer here

Correct Answer: 30.1

Deg^°

Rad