Special Right Triangles and Tangent

What is the length of y in this picture?

• 45

• 90

• 5

Find x.

• 12

• √2

• √3

• 6

The ratio in a right triangle of opposite to adjacent side is _____

• sine

• cosine

• tangent

• inverse cosine

Which equation would be used to solve for x?

• tan 44 = x/15

• cos 44 = x/15

• cos 44 = 15/x

• tan 44 = 15/x

Which equation would you use to solve for x?

• sin 62 = 10/x

• tan 62 = 10/x

• tan 62 = x/10

• cos 10 = x/62

I have been given the short leg in this 30-60-90 triangle.  How do I find the length of the hypotenuse?

• Multiply 4 by 2

• Multiply 4 by √3

• Multiply 4 by √2

• Divide 4 by √3

Solve for x and y in the special right triangle.

• y = 4, x = 4√3

• y = 4√2, x = 4√2

• y = 4 x = 12

• y = 8/√3, x = 16/√3

Answer explanation

The short leg (y) is half of the hypotenuse, so y = 4. The longer leg is √3 times the short leg, so x = 4√3.

In this 30-60-90 triangle, what is the length of the long leg?

• 6√2

• 3√3

• 12

• 6√3

Answer explanation

This is a 30°-60°-90° triangle, so n is half of 6 (n = 3), and m is √3 times n, so m = 3√3

What are the measures of the TWO acute angles in this slope triangle? (round to the nearest whole number)

• 38°

• 59°

• 31°

• 52°

Answer explanation

The slope is 3/5, so the lower angle is inverse tangent of 3/5, and the other acute angle is complementary (they add to 90°).

What type of triangles do you use the trig ratios with?

• any type

• right triangle

• obtuse triangle

• acute triangle