# Transcript: Calculations for an access ramp fill in the blanks activity

## Question 1:

Image of a right triangle. The height is 1, the base is 14, and the angle is indicated by a lowercase theta symbol.

What angle corresponds to a 1:14 gradient? Give your answer to two decimal points.

theta =

## Question 2:

Image of a right triangle. The height is 0.5 metres, the hypotenuse is x, and the angle is indicated by a lowercase theta symbol.

Using the angle found in question 1, if the entrance to the building sits 0.5 metres off the ground, how long will the ramp need to be? Round your answer to the nearest metre.

x =

## Hints:

### Calculating question 1:

Gradients are written as a ratio of the height of a right triangle over the length of the base, or the “rise over run”.

Because we know the value of the sides opposite and adjacent to our unknown angle, we can use the inverse tangent function to find the angle:

theta = inverse tangent function of (1 over 14)

theta = inverse tangent function of (0.0714)

theta = 4.09

### Calculating question 2:

Now that we know the value of the angle and the side opposite, we can use the sin formula to solve for the length of the ramp, which is the hypotenuse of the triangle:

sin of theta = opposite over hypotenuse

sin of (4.09) = .5 over x

0.0713 = .5 over x

0.0713 x = .5

x = .5 over 0.0713

x = 7.01 m which is approximately equal to 7 metres

## Answers:

**Question 1:**

theta =4.09 degrees

**Question 2:**

x = 7 metres