weapon of math destruction trig. day 1

it’s hard to read so

1) solve the following problems. Round segment lengths to four places past the decimal and angle measures to the nearest whole degree. For each problem, draw and label a picture and set up the appropriate trigonometry ratio.

2) how tall is a tree if it cast a shadow of 50 feet and the rays of the sun meet the ground at a 25° angle

3) A sonar operator on a battleship detects a submarine at a distance of 500 m horizontally at an angle of depression of 37°. How deep is the sub?

Question

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MrRoyal MrRoyal · Answer 1 · 2022-01-13T16:22:39+01:00

The questions are illustrations of trigonometry ratios and right triangles

Trigonometry ratio

Trigonometry ratios are very useful in determining the measure of angles, and the side lengths of a right triangle.

The value of x is calculated using the following sine trigonometry ratio

[tex]\sin(25) =\frac{5}{x}[/tex]

Make x the subject

[tex]x =\frac{5}{\sin(25)}[/tex]

This gives

[tex]x =11.8310[/tex]

Hence, the value of x is 11.8310

This question is illustrated by the first diagram in the attached figure

The height (h) of the tree is calculated using the following tangent trigonometry ratio

[tex]\tan(25) =\frac{h}{50}[/tex]

Make h the subject

[tex]h = 50 \times \tan(25)[/tex]

This gives

[tex]h = 23.3154[/tex]

Hence, the tree is 23.3154 feet tall

This question is illustrated by the second diagram in the attached figure

The depth (h) of the sub is calculated using the following tangent trigonometry ratio

[tex]\tan(37) =\frac{h}{500}[/tex]

Make h the subject

[tex]h = 500 \times \tan(37)[/tex]

This gives

[tex]h = 376.7770[/tex]

Hence, the depth of the sub is 376.7770 meters

Read more about trigonometry ratios at:

https://brainly.com/question/6241673