In a right triangle the leg opposite to the acute angle of 30 degrees in 7in. Find the hypotenuse and the other leg
2 answers:
Answer:
hypotenuse = 14inches
The other leg {adjacent} = 12.12inches
Step-by-step explanation:
To find the hypotenuse and the other leg which would be the adjacent of the triangle given the opposite to be 7inches, with opposite angle given as 30.
See attachment for illustration.
Therefore to find the hypotenuse we will apply the sine rule which says
a/sineA = b/sineB
Where a is line and A is its opposite angle same as b is line and B is its opposite angle.
So in this case:
a= 7inches, A = 30° , b = hypotenuse, B = 90° (angle at right angle).
Therefore we have,
7/sine30 = hypotenuse/sine90
Cross multiple
Hypotenuse*sine30 = 7*sine90
Hypotenuse = 7*sine90/sine30
Hypotenuse = 7*1/0.5
Hypotenuse = 7/0.5 = 14inches
Hypotenuse = 14 inches
Having gotten hypotenuse we can now find the other leg {adjacent} using the Pythagoras theorem, which says
Hypotenuse² = opposite² + adjacent²
adjacent² = Hypotenuse² - opposite²
adjacent² = 14² - 7²
adjacent² = 196 - 49
adjacent² = 147
adjacent = √147
adjacent = 12.1244 ~ 12.12inches
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Given:
First term of an arithmetic sequence is 2.
Sum of first 15 terms = 292.5
To find:
The common difference.
Solution:
We have,
First term:
Sum of first 15 terms:
The formula of sum of first n terms of an AP is
Where, a is first term and d is common difference.
Putting , n=15 and a=2 in the above formula, we get
Divide both sides by 15.
Dividing both sides by 7, we get
Therefore, the common difference is 2.5.