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PLEASE HURRY!! WILL GIVE BRAINLIEST
In the space below, use the law of sines or trigonometric ratios to find each length. Round your answer to 1 decimal place. (4 points total: 1 point each)
a. The length of the zip line, z
b. The height of the point on the tree where the top of the ladder rests against it, h
c. The distance between the base of the ladder and the base of the tree, b
d. The distance between the base of the tree and the spot where the zip line is anchored to the ground, B

PLEASE HURRY WILL GIVE BRAINLIEST In the space below use the law of sines or trigonometric ratios to find each length Round your answer to 1 decimal place 4 poi class=

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MrRoyal

Trigonometric ratios are useful in calculating the side lengths of a triangle.

  • The length of the zip line is 222.5 ft
  • The height where the ladder rests against the tree is 38.6 ft
  • The distance between the base of the ladder and that of the tree is 10.4 ft
  • The distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft

(a) Length, z

First we calculate (h) using the following sine ratio

[tex]\mathbf{sin(75) = \frac{h}{40}}[/tex]

Make h the subject

[tex]\mathbf{h = 40sin(75)}[/tex]

Next, we calculate (z) using the following sine ratio

[tex]\mathbf{sin(10)= \frac{h}{z}}[/tex]

Make z the subject

[tex]\mathbf{z= \frac{h}{sin(10)}}[/tex]

Substitute [tex]\mathbf{h = 40sin(75)}[/tex]

[tex]\mathbf{z= \frac{40sin(75)}{sin(10)}}[/tex]

[tex]\mathbf{z= 222.5 ft}[/tex]

Hence, the length of the zip line is 222.5 ft

(b) The height, h

In (a), we have

[tex]\mathbf{h = 40sin(75)}[/tex]

Evaluate

[tex]\mathbf{h = 38.6}[/tex]

Hence, the height where the ladder rests against the tree is 38.6 ft

(c) The distance, b

To do this, we make use of the following sine ratio

[tex]\mathbf{sin(15) = \frac{b}{40}}[/tex]

Make b the subject

[tex]\mathbf{b = 40sin(15)}[/tex]

[tex]\mathbf{b = 10.4}[/tex]

Hence, the distance between the base of the ladder and that of the tree is 10.4 ft

(d) Distance, B

To do this, we make use of the following sine ratio

[tex]\mathbf{sin(80) = \frac{B}{z}}[/tex]

Make B the subject

[tex]\mathbf{B = z\ sin(80)}[/tex]

Substitute [tex]\mathbf{z= 222.5 ft}[/tex]

[tex]\mathbf{B = 222.5\ sin(80)}[/tex]

[tex]\mathbf{B = 219.1}[/tex]

Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft

Read more about trigonometry ratios at:

https://brainly.com/question/24888715

iamchinchilla84
THIS IS FOR THE 25 FT LADDER NOT THE 40 FT LADDER!!! THE ALTERNATIVE!!!

The length of the zip line is 139.1 ft
The height where the ladder rests against the tree is 24.1 ft
The distance between the base of the ladder and that of the tree is 6.5 ft
The distance between the base of the tree and the spot where the zip line is anchored to the ground is 137.0 ft
(a) Length, z

First we calculate (h) using the following sine ratio
Sin(75)=h/25

Make h the subject
h=25sin(75)

Next, we calculate (z) using the following sine ratio
Sin(10)=h/z

Make z the subject
z=h/sin(10)

Substitute
h=25sin(75)
z= 25sin(75)/sin(10)
z=139.1 ft


Hence, the length of the zip line is 139.1 ft

(b) The height, h

In (a), we have
h=25sin(75)

Evaluate
h=24.1 ft

Hence, the height where the ladder rests against the tree is 24.1 ft

(c) The distance, b

To do this, we make use of the following sine ratio
sin(15)=b/40

Make b the subject
b=25sin(15)
b= 6.5 ft

Hence, the distance between the base of the ladder and that of the tree is 6.5 ft

(d) Distance, B

To do this, we make use of the following sine ratio
sin(80)=B/z

Make B the subject
B=z sin(80)

Substitute
z=139.1 ft
B=139.1 sin(80)
B=137.0 ft
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 137.0 ft


Credit to the person above me for the format <3

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