Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Half-Angle Identities: tan (A/2) = (sinA)/(1 + cosA)
cot (A/2) = (sinA)/(1 - cosA)
Use the Pythagorean Identity: cos²A + sin²B = 1
Use Unit Circle to evaluate: cos 45° = sin 45° = 
<u>Proof LHS → RHS</u>
Given: 
Rewrite Fraction: 
Half-Angle Identity: 
Substitute: 
Simplify: 




= 2
LHS = RHS: 2 = 2 
Answer:
Part 1) The ratio of the sides is 1.5
Part 2) see the explanation
Step-by-step explanation:
Part 1) we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
If Δdef and Δxyz are similar (given problem)
then
substitute the values

solve for FY

When two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
The scale factor is equal to

Part 2) How you could verify that these two triangles are indeed similar.
Remember that
In similar figures the corresponding angles are congruent
so
If
m∠D≅m∠X
m∠W≅m∠Y
m∠F≅m∠Z
then
Triangles are similar
The answer is FALSE hope this helps
Answer:
The value of the side PS is 26 approx.
Step-by-step explanation:
In this question we have two right triangles. Triangle PQR and Triangle PQS.
Where S is some point on the line segment QR.
Given:
PR = 20
SR = 11
QS = 5
We know that QR = QS + SR
QR = 11 + 5
QR = 16
Now triangle PQR has one unknown side PQ which in its base.
Finding PQ:
Using Pythagoras theorem for the right angled triangle PQR.
PR² = PQ² + QR²
PQ = √(PR² - QR²)
PQ = √(20²+16²)
PQ = √656
PQ = 4√41
Now for right angled triangle PQS, PS is unknown which is actually the hypotenuse of the right angled triangle.
Finding PS:
Using Pythagoras theorem, we have:
PS² = PQ² + QS²
PS² = 656 + 25
PS² = 681
PS = 26.09
PS = 26
So you have a diagram or picture of the triangle?
Anyways...
Answer: 36
Explanation:
3:5:7 is the ratio of the triangle's angles
The sum of all angles = 180 degrees.
3 + 5 + 7 = 15
Lets assume 'a' is the smallest angle with the ratio of 3
b is the second largest with a ratio of 5
And c is the largest angle with the ratio of 7
In other words:
a + b + c = 180
For 15 to get to 180 => 180 ÷ 15 = 12
So 15 × 12 = 180
So for 3 to get to a => 3 × 12 = 36
Thus the smallest angle is 36 degrees