Answer: 9.32 ft
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Cos α = adjacent side / hypotenuse
Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the adjacent side (x) is the distance between the bottom of the ladder and the house.
Replacing with the values given:
cos 39 = x/ 12
Solving for x
cos39 (12) =x
x= 9.32 ft
Feel free to ask for more if needed or if you did not understand something.
Answer:
The bottom of the ladder is 7.55 feet far away from the house
Step-by-step explanation:
To find the distance between the bottom of the ladder from a house if a ladder of 12 feet long is leaning against a house at an angle of 39°, then we will follow the steps below:
We can use trig ratios to find the solution to this problem
SOH CAH TOA
sinФ= opposite/hypotenuse
cosФ=adjacent/hypotenuse
tanФ=opposite /adjacent
from the diagram below;
angle Ф=39°
hypotenuse =12 feet
opposite = x where x is the distance of the bottom of the ladder from the house
Given these parameter, the best trig function to use sine
sinФ = opposite / hypotenuse
sin 39° =
cross-multiply
x = 12 sin 39
x ≈ 7.55 feet
Therefore, the bottom of the ladder is 7.55 feet far away from the house
Answer:
The volume of the similar prism is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x----> the volume of the larger prism
y----> the volume of the smaller prism
so
In this problem we have
-----> the scale factor
substitute and solve for x
Answer:
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).
Step-by-step explanation:
Our sample size is 96.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
Then, we need to subtract one by the confidence level and divide by 2. So:
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 95 and 0.025 in the t-distribution table, we have .
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
Now, we multiply T and s
For the lower end of the interval, we subtract the mean by M. So
For the upper end of the interval, we add the mean to M. So
The 95% confidence interval estimate for the mean highway mileage for SUVs is (18.29mpg, 20.91mpg).