Question

Solve the right triangle, ΔABC, for all the missing side and angles to the nearest tenth given sides a = 10.6 and b = 19.2.

Answer 1

A = 28.9 degrees, B = 61.1 degrees, c = 21.9

Explanation:

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Answer 2

Part 1)
`c=21.9\ units`

Part 2)
`B=61.1\°`

Part 3)
`A=28.9\°`

Part 4)
`C=90\°`

Explanation:

step 1

Find the length side c

Applying the Pythagoras Theorem

`c^(2)=a^(2)+b^(2)`

substitute the given values

`c^(2)=10.6^(2)+19.2^(2)`

`c^(2)=481`

`c=21.9\ units`

step 2

Fin the measure of angle B

we know that

In the right triangle

`tan(B)=b/a`

substitute the given values

`tan(B)=19.2/10.6`

`B=arctan(19.2/10.6)=61.1\°`

step 3

Find the measure of angle A

we know that

The measure of interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

Remember that in a right triangle the measure of angle C is 90 degrees

we have

`B=61.1\°`

`C=90\°`

substitute

`A+61.1\°+90\°=180\°`

`A=28.9\°`