For the given triangle, the tan of angle A equals C.
Step-by-step explanation:
Step 1:
For the given triangle, the hiking route is represented by AB and the change in elevation is represented by BC.
So we need to calculate the value of BC for the given triangle
Step 2:
In the given triangle, the opposite side has a length of 'a' feet, the adjacent side has a length of 'b' feet while the triangle's hypotenuse measures 400 feet.
To calculate the opposite side of the triangle, we can use the sine of any angle in that particular triangle. The sine of a particular angle is the opposite side's length divided by the hypotenuse's length.
sin A = [tex]\frac{oppositeside}{hypotenuse}[/tex] .
Step 3;
The length of the opposite side = a,
The length of the hypotenuse side = 400 units.
[tex]\sin A=\frac{a}{400}, \sin 25^{\circ}=0.4226[/tex]. So
[tex]0.4226=\frac{a}{400}, a=0.4226 \times 400[/tex] = 169.04 feet.
So the change in elevation is 169.04 feet.
