Question

Priya has planted a garden shaped like a right triangle. She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees . If Priya wants to build a fence around her garden. How many meters will she need? Round to the nearest hundredth and you must submit work to receive credit.

Answer 1

She will need 41.22 meters.

Explanation:

She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees .

The leg is adjacent to the hypothenuse. We know that the cosine of an angle
`\theta` is given by:

`cos(\theta) = (l)/(h)`

In which l is the length of the adjacent side and h is the hypothenuse.

Considering that we have
`\theta = 50, l = 11`, we can find the hypothenuse.

Looking at a calculator, the cosine of 50 degrees is 0.6428.

So

`0.6428 = (11)/(h)`

`0.6428h = 11`

`h = (11)/(0.6428)`

`h = 17.11`

The other leg:

In a right triangle, with legs
`l_1` and
`l_2`, and hypothenuse h, the pythagorean theorem states that:

`l_1^2 + l_2^2 = h^2`

We already have one of the legs and the hypothenuse, so:

`11^2 + l^2 = 17.11^2`

`l^2 = 17.11^2 - 11^2`

`l = √(17.11^2 - 11^2)`

`l = 13.11`

How many meters will she need?

This is the perimeter of the garden, which is the sum of its dimensions, of 11 meters, 13.11 meters and 17.11 meters. So

`P = 11 + 13.11 + 17.11 = 41.22`

She will need 41.22 meters.