76.8k views
3 votes
When instructed to find the length of HJ in right

triangle HJG, Alex wrote the equation

HJ

HJ

sin 28° = while Marlene wrote cos 62°

20

20

Are both students' equations correct? Explain

why.

H

+

20

28

O

G

1 Answer

5 votes

See attachement for the diagram of the triangle

Answer/Step-by-step explanation:

To find the length of HJ, we can use different equations as follows:

✔️Recall: SOHCAHTOA

Let's take <G as the reference angle = 28°

Opposite side to reference angle = HJ

Hypotenuse = 20

Apply SOH.

Thus:

Sin 28° = opp/hyp

Sin 28° = HJ/20 (Alex's equation is correct).

Solving further, we would have:

HJ = Sin 28 * 20 ≈ 9.4

✔️Another way is by using <H as the reference angle.

m<H = 180° - (90° + 28°) (sum of triangle)

m<H = 62°

Adjacent side to reference angle (<H) = HJ

Hypotenuse = 20

Apply CAH:

Cos 62° = Adj/Hyp

Cos 62° = HJ/20 (Marlene's equation is correct)

Solving further, we would have,

HJ = Cos 62° * 20 ≈ 9.4

As you can see, the equation of both students are correct. Both would arrive at the same answer using any of the two equations.

When instructed to find the length of HJ in right triangle HJG, Alex wrote the equation-example-1
User Alle
by
5.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.