Question

Find m/_I. I need help on solving this problem please?

Answer 1

60°

Explanation:

You want the measure of angle I in right triangle HIJ, given that the side opposite is 3√30 and the side adjacent is 3√10.

Tangent

The tangent relation is ...

Tan = Opposite/Adjacent

In this triangle, ...

tan(I) = (3√30)/(3√10) = √(30/10) = √3

Then the angle is ...

I = arctan(√3) = 60°

The measure of angle I is 60°.

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Additional comment

The trig functions of 30° and 45° and their relationships to each other are based on the side relationships of the two "special" right triangles:

30°-60°-90° triangle has side ratios 1 : √3 : 2

45°-45°-90° triangle has side ratios 1 : 1 : √2

Of course, side lengths are in the same order as their opposite angles.

The mnemonic SOH CAH TOA can help you remember the necessary relationships:

• Sin = Opposite/Hypotenuse
• Cos = Adjacent/Hypotenuse
• Tan = Opposite/Adjacent

Answer 2

∠ I = 60°

Explanation:

using the tangent ratio in the right triangle

tan I =
`(opposite)/(adjacent )` =
`(HJ)/(IJ)` =
`(3√(30) )/(3√(10) )` =
`(√(30) )/(√(10) )` =
`\sqrt{(30)/(10) }` =
`√(3)` , then

∠ I =
`tan^(-1)` (
`√(3)` ) = 60°