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

Answer:

She will need 41.22 meters.

Step-by-step 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:

$\cos{\theta} = \frac{l}{h}$

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

$0.6428 = \frac{11}{h}$

$0.6428h = 11$

$h = \frac{11}{0.6428}$

$h = 17.11$

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:

$11^2 + l^2 = 17.11^2$

$l^2 = 17.11^2 - 11^2$

$l = \sqrt{17.11^2 - 11^2}$

$l = 13.11$

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.