215k views
3 votes
HELP!!

Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
Figure shows right triangle W K J. Angle K is a right angle. The length of hypotenuse W J is 9.8 units. The measure of angle W is 21 degrees.

HELP!! Find the unknown measures. Round lengths to the nearest hundredth and angle-example-1

1 Answer

1 vote

Answer: Choice B

  • JK = 3.51
  • WK = 9.15
  • angle J = 69 degrees

========================================================

Step-by-step explanation:

Angle W = 21 degrees is the reference angle.

Opposite this reference angle is side JK.

The hypotenuse is WJ = 9.8

Use the sine ratio to connect the opposite and hypotenuse.

sin(angle) = opposite/hypotenuse

sin(W) = JK/WJ

sin(21) = JK/9.8

JK = 9.8*sin(21)

JK = 3.51200590554394 approximately

JK = 3.51 approximately

Make sure your calculator is in degree mode.

------------------------------

We can use the cosine ratio to determine side WK

cos(angle) = adjacent/hypotenuse

cos(W) = WK/WJ

cos(21) = WK/9.8

WK = 9.8*cos(21)

WK = 9.14908817967258 approximately

WK = 9.15 approximately

Or alternatively you can use the tangent ratio and solve for WK in the equation below

tan(21) = JK/WK

Yet another alternative is to use the pythagorean theorem

a^2+b^2 = c^2

With a = 3.51, b = unknown, and c = 9.8

You should get b = 9.15 after applying the pythagorean theorem. Once you know two sides of a right triangle, a bunch of options open up.

------------------------------

Angle J is found by subtracting the value of angle W from 90

W+J = 90

J = 90 - W

J = 90 - 21

J = 69 degrees

Or you could say

W+K+J = 180

21+90+J = 180

111+J = 180

J = 180-111

J = 69 degrees

But I prefer the first set of steps as it's faster.

You could use inverse trig functions to determine angle J, but it will require a calculator and it may not be as intuitive.

User DarrenMB
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.