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Answer:
(d) 71°
Step-by-step explanation:
The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.
<h3>Sine</h3>Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.
sin(W/2) = Opposite/Hypotenuse
sin(W/2) = (35/2)/(30) = 7/12
Using the inverse sine function, we find ...
W/2 = arcsin(7/12) ≈ 35.685°
W = 2×36.684° = 71.37°
W ≈ 71°
<h3>Law of cosines</h3>The law of cosines tells you ...
w² = u² +v² -2uv·cos(W)
Solving for W gives ...
W = arccos((u² +v² -w²)/(2uv))
W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°
W ≈ 71°
The answer : 4 sin c sin b sin a
Step by step
Formula = A+b+c = 180
B+c = 180-A
C+A= 180-B
A+B= 180-c
2 sin c • 2 cos a-b+c/ 2 cos a-b-c / 2
4 sin c cos 180-2b/2 cos a-(180-a)/ 2
4 sin c cos (90-b ) cos ( A-90)
4 sin c sin b sin A
Step by step
Formula = A+b+c = 180
B+c = 180-A
C+A= 180-B
A+B= 180-c
2 sin c • 2 cos a-b+c/ 2 cos a-b-c / 2
4 sin c cos 180-2b/2 cos a-(180-a)/ 2
4 sin c cos (90-b ) cos ( A-90)
4 sin c sin b sin A
Answer: Yes this is a right triangle
We can determine this by using the converse of the pythagorean theorem.
a = 5, b = 12, c = 13
Since those a,b,c values work in the pythagorean theorem, this proves we have a right triangle.