Question

The surveyor sets up the instrument to determine the height at the highest point on the hill. She determines that she is standing at a horizontal distance of 100 m and sights the top of the hill using an angle of 17°. i) Let ‘h' represent the height of the hill and ‘d' represent the horizontal distance. ii) Set up the appropriate trigonometric ratio to determine the height of the hill. iii) Replace the variables with the appropriate values.

Answer 1

`(a)\ h = d * \tan(\theta)`

`(b)\ h = 30.57m`

Explanation:

Given

`\theta = 17^o`

`d =100m`

`h = ??`

See attachment for illustration

Solving (a): Trigonometry ratio to calculate h.

From the attachment, we have:

`\tan(\theta) = (h)/(d)`

Multiply both sides by d

`d * \tan(\theta) = (h)/(d) * d`

`d * \tan(\theta) = h`

Rewrite as:

`h = d * \tan(\theta)`

Solving (b): The value of h

We have:

`\theta = 17^o`

`d =100m`

So:

`h = 100m * \tan(17^o)`

`h = 100m * 0.3057`

`h = 30.57m`