The bottom of the ladder on a horizontal flat surface rests against a wall. It makes an angle of elevation of 35°. The bottom of the ladder is 42 ft from the base of the wall. How long is the ladder? Round your answer to the nearest whole number. Do not include units.
routine right-triangle trig.
cos35° = 42/hypotenuse
hypotenuse = 42cos35 = 34.4 ft
to the nearest whole number, 34 ft
Final answer 300cm.
Pls teach me.
To find the length of the ladder, we can use trigonometry, specifically the trigonometric function of sine.
Let's break down the information provided in the question:
- The angle of elevation: The angle between the ladder and the horizontal flat surface is given as 35°.
- The distance from the base of the wall to the bottom of the ladder: This distance is given as 42 ft.
Since we have the angle of elevation, we can use the sine function. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the hypotenuse.
In this case, we can label the opposite side as the vertical distance from the ground to the top of the ladder and the hypotenuse as the length of the ladder.
Now, let's set up the equation using the sine function:
sin(35°) = Length of the ladder / 42 ft
To find the length of the ladder, we can rearrange the equation:
Length of the ladder = sin(35°) * 42 ft
Now we can calculate the value using a scientific calculator or trigonometric table:
Length of the ladder ≈ sin(35°) * 42 ft
Length of the ladder ≈ 0.5736 * 42 ft
Length of the ladder ≈ 24.07 ft
Rounding to the nearest whole number, we get the final answer:
The length of the ladder is approximately 24 feet.