Question

Need DESPERATE help! I'm taking a unit test for math (k12, 10th grade) I got 3 done already so here's the ones I missed: Question 5: Use the inverse sine to find the measure of J J<->L: 16 L<->K: 5 OPTIONS: 20.0, 19.4, 18.2, and 18.0 Question 6: ΔXYZ is a right triangle with right angle X, sin Y = m, and cos Y = k.What is cos Z − sin Z ? OPTIONS: m-k, 2m, k+m, k-m Question 7: Given, sin x (1161) and cos x (6061). What is tan x? OPTIONS: 61/60, 61/11, 11/60, 1 Question 8: ΔABC is a 30-60-90 triangle where m∠B = 90°. The length of the shorter leg is 11 units. What is the length of the hypotenuse? ______ units

Answer 1

Explanation:

Question 6)

sin Y= m

sin Y = m/1

So, hypotenuse is 1

Since sine is opposite over hypotenuse

So XZ= m and YZ = 1

Similarly, cos Y = k

cos Y = k/1

So adjacent side of angle Y is k

So XY = k

cos z - sin z =
`(XZ )/(YZ ) - (XY)/(YZ)`

cos z - sin z =
`(m )/(1 ) - (k)/(1)`

cos z - sin z = m - k

Question 7)

the relationship between sine, cosine, and tangent.

tan(x) = sin(x)/cos(x) = (11/61)/(60/61)

tan(x) = 11/60

Question 8)

Start with where the shorter leg is. It must be opposite the smallest angle.

In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it.

That being said, if the shortest side is x, the hypotenuse will be 2x.

Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22

The answer is 22