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
4.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.