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Furkat [3]
2 years ago
6

Help pls im being timed

Mathematics
1 answer:
Nitella [24]2 years ago
7 0

The trigonometric ratios show that the angle FHE is 48.59°.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypothenuse)^2=(leg_1)^2+(leg_2)^2. And the main trigonometric ratios are:

sin(\alpha) =\frac{opposite \;leg }{hypotenuse} \\ \\ cos(\alpha) =\frac{adjacent\;leg }{hypotenuse} \\ \\ tan(\alpha) =\frac{sin(\alpha )}{cos(\alpha )}= \frac{opposite \;leg }{adjacent\;leg } \\ \\

It is important to remember that the sum of internal angles for any triangle is 180°.

From the question, it is possible to see 2 right triangles (HGF and FHE).

You can find the hypotenuse of the triangle HGF from the  trigonometric ratio: sen Θ

sin45=\frac{opposite\; leg }{hypotenuse} =\frac{\sqrt8}{hypotenuse}\\ \\ \frac{\sqrt{2} }{2} =\frac{\sqrt{8} }{hypotenuse} \\ \\ \sqrt{2}*hypotenuse=2\sqrt{8} \\ \\ hypotenuse=\frac{2\sqrt{8} }{\sqrt{2}} =2\sqrt{4} =2*2=4

The hypotenuse of triangle HGF is one of legs for the triangle FHE. The, you can find the angle FHE from the  trigonometric ratio: tan β. Thus,

sin \beta =\frac{opposite\; leg }{adjacent\; leg} =\frac{3}{4}\\ \\ sin \beta=\frac{3}{4}=0.84806\\ \\ arcsin\beta =48.59^{\circ \:}

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

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Vesna [10]

Answer:

TU = 4.5units

Step-by-step explanation:

Since the pentagons are similar, hence the ratios of their similar sides will be equal to a constant.

Hence;

XY/ST = YZ/TU

Given the following

XY = 32

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ST = 4c + 2

TU = 5c + 2

Substitute into the expression as shown;

32/4c+2 = 36/5c+2

Cross multiply

36(4c+2) = 32(5c+2)

144c + 72 = 160c + 64

144c - 160c = 64 - 72

-16c = -8

c = -8/-16

c = 1/2

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TU =5(1/2) + 2

TU = 2.5 + 2

TU = 4.5

Hence the length of TU is 4.5units

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3 years ago
PLZ HELP ASAP. What is the measure of B?
KATRIN_1 [288]

Answer:

C. 55°

Step-by-step explanation:

Note the total measurement of angles for a triangle. The total measurement of all angles in a triangle = 180°

Note that m∠C is a right angle (as shown through the square), and that right angles = 90°

Subtract to find the measurement of the unknown angle (∠B)

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3 years ago
Read 2 more answers
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