i need to figure out how to write the formula for the following question In a right triangle a = 30 yds and t5an A = 2. Find b and c. I have the answers but do not know how to write the formula. Can you help me ?
Is that t5an A a typo? I assume it should read tan A = 2.
I don't know how your triangle is labeled but tan = side opposite the angle divided by side adjacent to the angle. One of those sides will be the 30 yards and you can solve for the other one. Then (one side)2 + (other side)2 = (hypotenuse)2
tanA = a/b = 2
(a is the side opposite A, and b is the side perpendicular to a.)
If a = 30, then b = a/2 = 15.
c = sqrt [(30^2 + (15)^2] = 33.54 yd
Certainly! To find the values of b and c in a right triangle with given values for angle A and side a, you can use the trigonometric ratios sine, cosine, and tangent.
In this case, you are given that tan(A) = 2 and a = 30 yards. Assuming A is one of the acute angles, we can use the definition of tangent:
tan(A) = opposite/adjacent
In a right triangle, the side opposite angle A is b, and the side adjacent to angle A is c. So we can rewrite the equation as:
tan(A) = b/c
Since tan(A) is given as 2, we have:
2 = b/c
Now, to find the values of b and c, you need one more equation involving these variables. You mentioned that a = 30 yards. In a right triangle, the Pythagorean theorem can be used:
a^2 = b^2 + c^2
Substituting the given value of a:
(30)^2 = b^2 + c^2
Simplifying this equation, you have a system of two equations:
2 = b/c (Equation 1)
900 = b^2 + c^2 (Equation 2)
Using these equations, you can solve for the values of b and c. You have two options to do so:
1. Use substitution method: Solve Equation 1 for b and substitute it into Equation 2. Then solve the resulting equation for c, and finally substitute the value of c back into Equation 1 to find b.
2. Use elimination method: Rearrange Equation 1 to b = 2c, and substitute this expression for b into Equation 2. Then simplify the equation and solve for c. Once you have the value of c, substitute it back into Equation 1 to find b.
Both methods should yield the same solution for b and c in the right triangle.