Question

Suppose That In Triangle ABC,A=65∘,B=35∘, And A=15 Feet. Find The Remaining Angle And Sides. Round Your Answers To One Decimal Place. B= ? Feet C= ? Feet C = ow many degrees?

Answer 1

Sure, let's solve this step by step.

First, we know that in any triangle, the sum of the angles is 180 degrees. So, we can calculate the third angle by subtracting the given angles from 180. This gives us:

C_angle = 180 - A_angle - B_angle
= 180 - 65 - 35
= 80 degrees

So, the remaining angle, ∠C, is 80 degrees.

For calculating the remaining sides, we need to use the Law of Sines. The formula for the Law of Sines is:

a / sin(A) = b / sin(B) = c / sin(C)

Here, a, b, c are the sides of the triangle opposite to angles A, B, C respectively. We can re-arrange this formula to find the other sides in terms of side a and corresponding angles.

For side B, the formula becomes:

B_side = (A_side*sin(B_angle)) / sin(A_angle)
= (15*sin(35)) / sin(65)

On calculating this, we get B_side = 9.5 feet

Similarly, for side C, the formula becomes:

C_side = (A_side*sin(C_angle)) / sin(A_angle)
= (15*sin(80)) / sin(65)

On calculating this, we get C_side = 16.3 feet

So, the remaining sides and angles of the triangle ABC are - ∠C = 80 degrees, Side B = 9.5 feet and Side C = 16.3 feet. All values are rounded to one decimal place for simplicity.