Which equation below is equivalent to $\sin C=\frac{h}{a} ?$
A. $h=\frac{\sin C}{a}$
B. $a=h \sin C$
C. $a=\frac{\sin C}{h}$
D. $h=a \sin C$
Answer (1)
To find an equivalent equation to sin C = a h , we follow these steps:
Multiply both sides of the equation by a : a sin C = h .
Rewrite the equation: h = a sin C .
The equivalent equation is: h = a sin C .
Explanation
Analyze the problem We are given the equation sin C = a h and asked to find an equivalent equation from the given options.
Multiply both sides by a To find an equivalent equation, we can manipulate the given equation using algebraic operations. In this case, we can multiply both sides of the equation by a .
Simplify the equation Multiplying both sides of sin C = a h by a gives us:
a ⋅ sin C = a ⋅ a h
a sin C = h
This can be rewritten as:
h = a sin C
Compare with the options Now, we compare the derived equation h = a sin C with the given options:
h = a s i n C (Incorrect)
a = h sin C (Incorrect)
a = h s i n C (Incorrect)
h = a sin C (Correct)
State the final answer The equation equivalent to sin C = a h is h = a sin C .
Examples
Understanding trigonometric relationships like sin C = a h is crucial in various real-world applications. For instance, when designing a ramp, you can use this relationship to determine the height ( h ) of the ramp given the angle of elevation ( C ) and the length of the ramp ( a ). This ensures the ramp is safe and meets accessibility standards. Similarly, in surveying, this relationship helps calculate heights of buildings or mountains using angles and distances.
