Question

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Answer 1

Known Values Angle A = 90°
Side c = 4
Angle B = 25°
Step #1: Find angle C by subtracting the other 2 angles from 180°.
C = 180° - A° - B°
C = 180° - 90° - 25°
C = 65°
Step #2: Use the Law of Sines to find side a.
a / sin(A) = c / sin(C)
a / sin(90°) = 4 / sin(65°)
a = (sin(90°) x 4) / sin(65°)
a = 4.414
Step #3: Use the Law of Sines to find side b.
b / sin(B) = c / sin(C)
b / sin(25°) = 4 / sin(65°)
b = (sin(25°) x 4) / sin(65°)
b = 1.865
So you have the sides
c = 4
b = 1.865
a = 4.414

The perimeter is all the sides added up
P = 4 + 1.865 + 4.414
P = 10.279
That can be rounded to 10.3 units

Hope this helps!

Answer 2

Answer:
10.3 units

Step-by-step explanation:
Triangle ABC is a right-angled triangle. This means that we can apply special trig functions.
We are given that:
angle B = 25 degrees and AB = 4 units
Therefore:
cos(B) = adjacent / hypotenuse
cos(25) = 4 / BC
BC = 4.414 units
tan(B) = opposite / adjacent
tan(25) = AC / 4
AC = 1.865

Finally, we can get the perimeter as follows:
perimeter = AB + BC + AC
perimeter = 4 + 4.414 + 1.865
perimeter = 10.279 which is approximately 10.3 units

Hope this helps :)