Geo please help I have two question!

Step-by-step explanation:

From the given right angle triangle,

the hypotenuse of the right angle triangle is 13

With m∠65° as the reference angle,

y represents the adjacent side of the right angle triangle.

x represents the opposite side of the right angle triangle.

To determine the value of x, we would apply the sine trigonometric ratio which is expressed as

Sin θ = opposite side/hypotenuse. Therefore,

Sin 65 = x/13

x = 13Sin65 = 13 × 0.906

x = 11.8 to the nearest tenth

Step-by-step explanation:

This is classic right triangle trig.  

Begin by making sure you know which side is which of a triangle.  That means, in short, make sure you know for a fact which side is the hypotenuse!  We have an angle and are asked to find out what the measure of side x is.  We are given that the hypotenuse is 13.  You should ask yourself, "How is side x related to the given angle?"  Side x is opposite the given angle.  So now that we know we are dealing with the side opposite the angle and the hypotenuse, this is the sin ratio.  Sin of an angle is equal to the opposite side over the hypotenuse:

 and

13sin65 = x so

x = 11.8

Now for y.  Ask yourself, "How is side y related to the given angle?"  We have already established that 13 is the length of the hypotenuse, so side y cannot be the hypotenuse.  It must be the side adjacent, which means "next to".  The side adjacent and the hypotenuse are the cos of the angle.  The cosine of an angle is equal to the side adjacent over the hypotenuse:

 and

13cos65 = y so

y = 5.5

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.