Slope and Tangent with Special Right Triangles

• 30°

• 45°

• 55°

• 60°

Answer explanation

In this case, the rise of the ramp is the opposite of the angle (rise = opposite) and the run of the ramp is adjacent to the angle (run = adjacent), so the angle is the inverse tangent of the slope.

The slope of the hypotenuse of this triangle is approximately:

• 12

• 0.36

• 2.75

Answer explanation

In this case, rise/run is the same as opposite/adjacent, so the slope is the tangent of the angle (tan 20°=0.36).

The tangent of the acute angle of a triangle is always equal to the slope of the hypotenuse.

• True
• False

Answer explanation

In this case, the slope of the hypotenuse is equal to tan (A), but it is not equal to tan (B)--that would be run/rise.

Find x.

• 10
• √3
• 5
• 10√3

Answer explanation

The short leg in a 30°-60°-90° triangle is half of the hypotenuse, so x = 5.

Tags

CCSS.HSG.SRT.C.8

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.

Tags

CCSS.HSG.SRT.C.8

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 is the equation of this line?

• y = 5/3x

• y = 3x + 5

• y = 5x +3

• y = 3/5x

Answer explanation

The slope is 3/5 and the y-intercept is 0. The equation of a line is y = mx +b.

What is the length of y in this picture?

• 45
• 5√2
• 90
• 5

Answer explanation

This is a 45°-45°-90° Triangle, so y = 5.

Tags

CCSS.HSG.SRT.C.8

What is the length of x in this 45-45-90 triangle?

• 4√2
• 4
• 8
• 4√3

Answer explanation

This is a 45°-45-90 Triangle, so y = 4, and x = 4√2.

Tags

CCSS.8.G.B.8

Find the equation of this line.

• y = 1.5x + 2

• y = 2x + 2

• y = 2.5x + 2

• y = 3x + 2

Answer explanation

The y-intercept is 2. The slope is the tangent of the angle: tan(56.31) = 1.5. So the equation is

y = 1.5x + 2.