How do you solve this??

40 pts and Brainliest pls give detailed answer :)

horsena [70]

Answer:

58 ft

Step-by-step explanation:

So I attached a diagram that illustrates the triangle that is formed. We know an angle, as well as the hypotenuse. We are looking for the height, or in other words the opposite side of the angle. There is a trigonometric function defined as: $sin(\theta) = \frac{opposite}{hypotenuse}$ . Using this we can plug in known values and solve for the opposite side, which I'll simply represent as x.

$sin(46) = \frac{x}{80}$

Multiply both sides by 80

$sin(46) * 80 = x$

Calculate sin(46) using a calculator (make sure it's in degree mode)

$0.7193398 * 80 = x$

Simplify

$57.547 \approx x$

Round this to the nearest foot

$58 \approx x$

4 0

2 years ago

Four times the difference of a number and 3 is the same as 3 increased by four times the number plus three times the number. Fin

motikmotik

Answer:

-2 = n

Step-by-step explanation:

-3 + 4n = 4n + 3 + 3n

-3 + 4n = 7n + 3 [Combine like-terms]

-7n -7n

________________

-3 - 3n = 3

+3 +3

________________

-3n = 6

n = -2

I am joyous to assist you anytime.

4 0

4 years ago

In the diagram shown, /Il m, m

Dmitry_Shevchenko [17]

Answer:

29°

Step-by-step explanation:

Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.

m∠1 = m∠8

3x+25 = 4x-17

42 = m . . . . . . . . add 17-3x

Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...

m∠2 = 180° -151° = 29°

5 0

4 years ago

I NEED HELP WILL GIVE BRAINLIEST!! PLEASE HELP ME ASAP!!!!

GenaCL600 [577]

Answer:

A. The length of the second leg is 8.5 inches

B. The length of the three-dimensional diagonal is 9.9 inches

Step-by-step explanation:

Let us revise the relation between the hypotenuse and the two legs of a right triangle

(hypotenuse)² = (vertical leg)² + (horizontal leg)²

∵ The length of the rectangular box = 8 inches

∵ The width of the rectangular box = 3 inches

∵ The height of the rectangular box = 5 inches

∵ Length and width are perpendicular to each other

∴ The Δ whose legs are 3 and 8 is a right triangle

In the right Δ whose legs are 3 and 8

∵ (hypotenuse)² = (3)² + (8)²

∴ (hypotenuse)² = 9 + 64

∴ (hypotenuse)² = 73

- Take √ for both sides

∴ hypotenuse = $\sqrt{73}$ = 8.544003745

- Round it to the nearest tenth of one inch

∴ hypotenuse = 8.5 inches

A.

The 3-dimensional diagonal is the hypotenuse of a right triangle whose legs are the vertical edge and the hypotenuse of the right triangle whose legs are 3 and 8

∵ The hypotenuse of the right triangle whose legs are 3 and

8 is 8.5 inches

∴ The length of the second leg is 8.5 inches

B.

In the right triangle whose hypotenuse is the 3-dimensional diagonal and legs are the vertical edge , the hypotenuse of the right triangle whose legs are 3 and 8

∵ (3-dimensional diagonal)² = (5)² + (73)²

∴ (3-dimensional diagonal)² = 25 + 73

∴ (3-dimensional diagonal)² = 98

- Take √ for both sides

∴ 3-dimensional diagonal = $\sqrt{98}$ = 9.899494937