Do i treat side c as the opposite or hypotenuse when my only given angle is 90 degrees?

Question

I have a right triangle with the only given angle being 90 and 2 side lengths: hypotenuse(c) 4.889 and adjacent(b) 1.69. I need to solve the triangle. If the hypotenuse is opposite my angle (90), how do i determine which trig function to use in solving?

Answer 1

Hi Maddie!

Hopefully this formats ok!

The hypotenuse is the side opposite the right angle

(the longest side). You have the adjacent side and

hypotenuse. Cosine uses the adjacent side and hypotenuse.

adj

cosΘ = ----

hyp

You probably have one of the following scenarios for your triangle.

|-_

| -_ (hyp)

| opp -_4.889 1.69

| _ -_ for this one, cosΘ = ------ ≈ .34567

|_ |______Θ__-_ 4.889

1.69

(adj) so Θ ≈ cos^-1(.34567) ≈ 69.78°

| -_

|Θ -_ (hyp)

1.69 | - _ 4.889 The computation for this one is the same

(adj) |__ -_ for Θ, it is just in a different location.

|__|______-_

(opp)

The other angle can be figured, since all the sides of

a triangle add to 180°.

The other side can be found using sine.

opp

sinΘ = ----

hyp

You know the value of Θ, so can figure sinΘ

Solving for the opposite side, you have the

equation:

opp = hyp * sinΘ

See if you can find out the other angle and

the opposite side from this information.

Answer 2

the angle B has sinB=1.69/4.889 ,,,,,,,b is opposite to angle B

find B=sin^-1(1.69/4.889)

A=90-B

side a=√(4.889²-1.69²)

you can check

sinA=a/c=a/4.889

A=sin^-1(a/4.889)