By using trigonometric identity, the value of a, x, b, n and m are 12.3, 9.3, 6.6, 4.6 and 6.9, respectively
How to solve this problem
To solve this problem, use trigonometric identity
To find a, Cos 35° = a/16
Cross multiply
a = cos 35° * 16
Now, evaluate cos 35°. Using a calculator or trigonometric tables, find that cos 35° ≈ 0.819.
Substituting the value:
16 * 0.819 =12.304
Therefore, a ≈ 12.304.
To find x, tan 65° = 20/x
To isolate "x", take the reciprocal of both sides of the equation:
1 / (tan 65°) = x / 20
Now, evaluate the value of tan 65°. Using a calculator or trigonometric tables, we find that tan 65° ≈ 2.1445.
Substituting the value:
1 / 2.1445 = x / 20
To solve for "x", multiply both sides of the equation by 20:
20 / 2.1445 = x
x ≈ 9.326
To find b, Sin 73° = b/7
Multiply both sides by 7:
7 * sin 73° = b
Now, evaluate sin 73°. Using a calculator or trigonometric tables, we find that sin 73° ≈ 0.948.
Substituting the value:
7 * 0.948 = 6.636
Therefore, b ≈ 6.636.
To find n, Sin 60° = 4/n
To isolate "n", take the reciprocal of both sides of the equation:
1 / (sin 60°) = n / 4
Now, evaluate the value of sin 60°. Using a calculator or trigonometric tables, we find that sin 60° = √3/2 ≈ 0.866.
Substituting the value:
1 / 0.866 = n / 4
To solve for "n", we can multiply both sides of the equation by 4:
4 / 0.866 = n
n ≈ 4.619
To find m, Tan 60 = m/4
Multiply both sides by 4:
4 * tan 60° = m
Now, evaluate the value of tan 60°. Using a calculator or trigonometric tables, we find that tan 60° = √3 ≈ 1.732.
Substituting the value:
4 * 1.732 = 6.928
Therefore, m ≈ 6.928.