SOLUTION: A triangle has an angle of 0.75 rads, and an opposite side of 47 meters. Find the lengths of the remaining side if possible.

Question 958703: A triangle has an angle of 0.75 rads, and an opposite side of 47 meters. Find the lengths of the remaining side if possible.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
one angle and the opposite side is not enough to get a particular triangle.

you need at least 2 angles and 1 side opposite one of the angles.

then you can use the law of sines to find the length of the other sides.

you need at least 2 sides and 1 angle between them.

then you can use the law of cosines to find the third side and the other angles.

the attached diagram shows at least 3 triangles that have the same angle with the same length of side opposite it.

there are many others.

$$$

you would use the law of sines with these triangles to find the other angles and the length of the other sides.

the law of sines is:

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

a is the side opposite angle A.
b is the side opposite angle B.
c is the side opposite angle C.

With 2 angles and the side opposite one of them, you can find the other two angles and the length of the other two sides easily.

In the middle diagram, where the points of the triangle are labeled:

side a would be side BC which is opposite angle A.
side b would be side AC which is opposite angle B.
side c would be side AB which is opposite angle C.
if you have the length of 2 sides and the measure of the angle between them, you can use the law of cosines.

the law of cosines is:

c^2 = a^2 + b^2 - 2 * a * b * cos(C).

RELATED QUESTIONS
A triangle has angles 0.21 rads and 0.58 rads, with the intermediate side of length 16... (answered by Alan3354)

A right triangle has an angle of 0.75 radians . If the hypothenuse is 5 meters, find the... (answered by lwsshak3)

an angle bisector of a triangle divides the opposite side of the triangle into segments (answered by Edwin McCravy)

A right triangle has a hypotenuse of 5 meters and an opposite of 4 meters. find the angle (answered by lwsshak3)

An arc has an angle 0.8 rads and arclength 4.8 meters. Find the... (answered by nerdybill)

Use the figure. Find the lengths of the remaining sides of the triangle. See Example 7.... (answered by MathLover1,MathTherapy)

Use the figure. Find the lengths of the remaining sides of the triangle. See Example 10.... (answered by mananth,MathTherapy)

A triangle has an angle of 0.61 radians. If the opposite is 13 meters, find the length of (answered by lwsshak3)

Find the altitude of an equilateral triangle, if each side of the triangle has a length... (answered by palanisamy)