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3 years ago

The national weather service reports the daily temperature in degrees

Mathematics

1 answer:

kobusy [5.1K]3 years ago

4 0

Answer:

$C =\frac{5}{9}(F - 32)$

Step-by-step explanation:

Given

$F = 1.8C + 32$

Required

Solve for C

$F = 1.8C + 32$

Subtract 32 from both sides

$F-32 = 1.8C + 32-32$

$F-32 = 1.8C$

Divide both sides by 1.8

$\frac{1}{1.8}(F - 32) = C$

Express the decimal as fraction

$\frac{1}{18/10}(F - 32) = C$

$\frac{10}{18}(F - 32) = C$

Simplify

$\frac{5}{9}(F - 32) = C$

$C =\frac{5}{9}(F - 32)$

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2 years ago

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Nitella [24]

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,

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