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

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.

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Thu Nguyệt 3 years 2021-08-04T05:04:31+00:00 1 Answers 53 views 0

Answers ( )

  1. bonexptip
    0
    2021-08-04T05:06:13+00:00
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    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.

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