Question

NEED HELP ON HELP ON HOW TO DO THIS

You have triangle JKL. Angle J is a right triangle. Angle K has a measure of 40 degrees. Side k=26. Solve the triangle. Round angles and sides to nearest tenth.

Answer choices:

A) Angle L= 50 degrees, side L= 31.0, side J= 40.4

B) Angle L= 50 degrees, side L= 33.3, side J= 42.8

D) Angle L= 50 degrees, side L= 21.8, side J= 33.9

E) Angle L= 50 degrees, side L= 33.9, side J= 21.8

Pls give explanation!!

Answer 1

Option E

Step by step explanation:

We know that angle J is a right angle meaning it's an angle 90 degrees. So to find angle L;

90+40+L=180

130+L=180

L=180-130

So therefore angle L =50 degrees

Now to find side J which is the opposite in the triangle,we use tan because it has adjacent and opposite which is what we're looking for;

Tan 40 degrees =opposite/26

We cross multiply

Opposite =Tan 40 degrees×26

Opposite =21.8

Side J=21.8

With side J found we can find side L using Pythagoras theorem

L^2=21.8^2 +26^2

L^2=475.24+676

L^2=1,151.24

L=Square root of 1,151.24

L=33.9

Answer 2

A) Angle L= 50 degrees, side L= 31.0, side J= 40.4

Explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. The given side of k is opposite the given angle K, so the sine or tangent functions can be used to find missing sides. If we want to start with the hypotenuse, we can use the relation ...

Sin = Opposite/Hypotenuse

sin(40°) = 26/j

j = 26/sin(40°) ≈ 40.4 . . . units (matches choice A)

Similarly, we can use the tangent relation to find side ℓ:

Tan = Opposite/Adjacent

tan(40°) = 26/ℓ

ℓ = 26/tan(40°) ≈ 31.0 . . . units (matches choice A)

Of course, angle L is the complement of 40°:

L = 90° -40° = 50°

The solution to the triangle is L = 50°, ℓ = 31.0, j = 40.4.