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3 years ago

In PQR the measure of R=90 the measure of P=62 and RP=8.6 find the length of QR to the nearest tenth of a foot.

Mathematics

1 answer:

alex41 [277]3 years ago

5 0

Answer:

QR = 4.6 ft

Step-by-step explanation:

By applying tangent rule in the given triangle PQR,

tan(62°) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

= $\frac{8.6}{QR}$

QR = $\frac{8.6}{\text{tan}(62)}$

QR = 4.573

QR ≈ 4.6 ft

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Answer:

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3 years ago

The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer l

Licemer1 [7]

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

<u>Pythagorean Theorem</u>

$c^2 = a^2 + b^2$

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a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

$c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x$

Now let's factorize to get solutions for x.

$0 = x(x-20)$

First solution:

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Second solution:

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Since a side of a triangle has to be a positive number, x is equal to 20.

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