To solve this problem, we just need to set up a simple equation. We have that angles 1 and 2 add up to equal a right angle, or 90°, and that m<2 is 35°, so we just have to do a bit of subtraction.
<1 + <2 = 90 Given
<1 + 35 = 90 Substitute 35 for <2
<1 = 55° Subtract 35 from both sides to get rid of it, since subtraction is the opposite of addition.
Therefore, m<1 = 55°.
Hope this helps!
7,500*20%=g
7,500*.20=g
1500=g
1,500 general admission tickets were sold.
Answer:
depth of swimming pool = 2.4 meters
Step-by-step explanation:
Volume of the swimming pool = l x b x h = 3000
Volume of the swimming pool = 50 x 25 x h = 3000
h = 2.4 meters
Given:
![\tan A=\dfrac{1}{5}](https://tex.z-dn.net/?f=%5Ctan%20A%3D%5Cdfrac%7B1%7D%7B5%7D)
![\tan B=\dfrac{1}{4}](https://tex.z-dn.net/?f=%5Ctan%20B%3D%5Cdfrac%7B1%7D%7B4%7D)
To find:
The value of
.
Solution:
We know that,
![\tan (A-B)=\dfrac{\tan A-\tan B}{1+\tan A\tan B}](https://tex.z-dn.net/?f=%5Ctan%20%28A-B%29%3D%5Cdfrac%7B%5Ctan%20A-%5Ctan%20B%7D%7B1%2B%5Ctan%20A%5Ctan%20B%7D)
Putting the given values, we get
![\tan (A-B)=\dfrac{\dfrac{1}{5}-\dfrac{1}{4}}{1+\dfrac{1}{5}\cdot \dfrac{1}{4}}](https://tex.z-dn.net/?f=%5Ctan%20%28A-B%29%3D%5Cdfrac%7B%5Cdfrac%7B1%7D%7B5%7D-%5Cdfrac%7B1%7D%7B4%7D%7D%7B1%2B%5Cdfrac%7B1%7D%7B5%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B4%7D%7D)
![\tan (A-B)=\dfrac{\dfrac{4-5}{20}}{1+\dfrac{1}{20}}](https://tex.z-dn.net/?f=%5Ctan%20%28A-B%29%3D%5Cdfrac%7B%5Cdfrac%7B4-5%7D%7B20%7D%7D%7B1%2B%5Cdfrac%7B1%7D%7B20%7D%7D)
![\tan (A-B)=\dfrac{\dfrac{-1}{20}}{\dfrac{20+1}{20}}](https://tex.z-dn.net/?f=%5Ctan%20%28A-B%29%3D%5Cdfrac%7B%5Cdfrac%7B-1%7D%7B20%7D%7D%7B%5Cdfrac%7B20%2B1%7D%7B20%7D%7D)
![\tan (A-B)=\dfrac{-1}{21}](https://tex.z-dn.net/?f=%5Ctan%20%28A-B%29%3D%5Cdfrac%7B-1%7D%7B21%7D)
Taking square on both sides, we get
![\tan^2 (A-B)=\left( \dfrac{-1}{21}\right)^2](https://tex.z-dn.net/?f=%5Ctan%5E2%20%28A-B%29%3D%5Cleft%28%20%5Cdfrac%7B-1%7D%7B21%7D%5Cright%29%5E2)
![\tan^2 (A-B)=\dfrac{1}{441}](https://tex.z-dn.net/?f=%5Ctan%5E2%20%28A-B%29%3D%5Cdfrac%7B1%7D%7B441%7D)
Therefore, the value of
is
.