A 19-ft ladder leans against a building so that the angle between the ground and the ladder is 80∘.
How high does the ladder reach on the building?
I did 19sin(80) to get me 18.76847847 for how high the ladder reach on the building... but when i put the answer, it's wrong.
Any help would be awesome!
To find out how high the ladder reaches on the building, you need to use the trigonometric function cosine, not sine.
The vertical height, which is the side opposite to the angle between the ground and the ladder, is given by the formula:
vertical height = ladder length × cosine(angle)
Using your given values, the ladder length is 19 ft and the angle is 80 degrees. Plugging these values into the formula, we get:
vertical height = 19 ft × cosine(80°)
Calculating this, we find:
vertical height ≈ 19 ft × 0.17364817766693033
≈ 3.2919349322465737
Therefore, the ladder reaches approximately 3.29 ft high on the building.
To find how high the ladder reaches on the building, you are correct in using the sine function. The mistake might be due to rounding off the result. Let's go through the calculation step by step.
Given:
Ladder length = 19 ft
Angle between the ground and the ladder = 80°
To find the height reached by the ladder on the building using trigonometry, we will use the sine function.
Step 1: Convert the angle from degrees to radians.
Since trigonometric functions typically work with angles in radians, we need to convert 80° to radians. To convert degrees to radians, we use the formula:
Radians = Degrees × π / 180
By substituting the value of the angle into the formula, we get:
Radians = 80 × π / 180
Simplifying this further, we find:
Radians ≈ 1.3962634
Step 2: Calculate the height reached by the ladder on the building.
To determine the height reached by the ladder on the building, we need to multiply the length of the ladder by the sine of the angle.
Height = Ladder Length × sin(Angle)
Substituting the values, we have:
Height = 19 ft × sin(1.3962634)
Using a calculator, we can evaluate the sine function and get the result:
Height ≈ 18.76847847 ft
Now, it's crucial not to round off the result until the final step because rounding off too soon can introduce errors.
So, if you rounded off to 18.76847847 feet and it was marked as incorrect, it could be due to the precision required in the answer. Try rounding the answer to the appropriate number of decimal places specified in the question or check if there are any formatting errors while entering the answer.
If rounding is the issue, round the answer to the nearest hundredth (i.e., two decimal places):
Height ≈ 18.77 ft
Try submitting this rounded answer and see if it is marked as correct.