Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

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Answer 1

Hello!

Let's take this problem in steps

First image

--> angle A = 30 degrees

--> length of a = 6

==> using trigonometry, the relationship between side opposite angle

A and the hypotenuse is:

`sin(A)=(a)/(x) \\\\sin(30)=(6)/(x) \\\\(1)/(2)=(6)/(x) \\\\x=12`

Second image

--> angle A = 21 degrees

--> length of c = 8

==> using trigonometry, the relationship between the side opposite

angle A and the hypotenuse is:

`sin(A)=(x)/(c) \\\\sin(21)=(x)/(8) \\\\0.358=(x)/(8) \\\\x=0.358*8\\\\x=2.864\\\\x \approx 2.9`

Third image:

--> angle A = 55 degrees

--> length of C = 8

==> using trigonometry, the relationship between the side adjacent

angle A and the hypotenuse is:

`cos(A)=(x)/(c) \\\\\\cos(55)=(x)/(8) \\\\\\0.573=(x)/(8)\\ \\x=0.573*8\\\\x=4.584\\\\x \approx 4.6`

Answer

• First Image: 12
• Second Image: 2.9
• Third Image: 4.6