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2 years ago

Solve the right triangle. Round decimals to the nearest tenth

Mathematics

1 answer:

Tems11 [23]2 years ago

8 0

Answer:

j = 19.6

k = 25.9

J = 49°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.

<h3>Analysis</h3>

The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...

Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin

Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan

Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.

<h3>Application</h3>

Hypotenuse = Opposite/Sin

IJ = 17/sin(41°) ≈ 25.9

Adjacent = Opposite/Tan

IK = 17/tan(41°) ≈ 19.6

Angle J = 90° -41° = 49°

In summary, ...

j = 19.6

k = 25.9

J = 49°

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