Since they're vertical angles, they're equal in degree measure
since they're equal, we can make the two expressions equal to each other
5a - 1 = 2a + 20
add 1 to both sides
5a = 2a + 21
subtract 2a from both sides
3a = 21
divide both sides by 3a
a = 7
now, plug the answer you found for a into one of the two expressions
5a - 1 becomes (5*7) - 1, which equals 34
to double check that they're equivalent (since they're vertical angles)
2a + 20 becomes (2*7) + 20, which equals 34
both angles are 34 degrees!
Answer:
57/26 or 2 5/26
Step-by-step explanation:
Answer:
The height of the tree is Greater than 50 feet, so Iva’s house is not safe
Step-by-step explanation:
Find the height of the tree
Let
h ----> the height of the tree
we know that
The tangent of angle of 50 degrees is equal to divide the opposite side to the angle of 50 degrees (height of the tree) by the adjacent side to the angle of 50 degrees (tree’s distance from the house)
so
tan(50°)=h/50
h=(50)tan(50°)=59.6 ft
therefore
The height of the tree is Greater than 50 feet, so Iva’s house is not safe
The value of line AL is 21. 51cm
<h3>How to determine the length</h3>
To find line AL,
Using
Sin α = opposite/ hypotenuse to find line AB
Sin 90 = x/ 24
1 = x/24
Cross multiply
x = 24cm
Now, let's find line AC
Sin angle B = line AC/24
Note that to find angle B
angle A + angle B + angle C = 180
But angle B = 2 Angle A
x + 2x + 90 = 180
3x + 90 = 180
3x = 180-90
x = 30°
Angle B = 2 × 30 = 60°
Sin 60 = x/ 24
0. 8660 = x/24
Cross multiply
x = 24 × 0. 8660
x = 20. 78cm
We have the angle of A in the given triangle to be divide into two by the bisector, angle A = 15°
To find line AL, we use
Cos = adjacent/ line AL
Cos 15 = 20. 78/ line AL
Line AL = 20. 78/ cos 15
Line AL = 20. 78 / 0. 9659
Line AL = 21. 51 cm
Thus, the value of line AL is 21. 51cm
Learn more about trigonometry ratio here:
brainly.com/question/24349828
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Answer:
-2 7/12
Step-by-step explanation:
When the negative number is being subtracted, it is like adding, but you HAVE TO KEEP THE NEGATIVE SIGN. In this case, -1 9/12 plus -10/12 would be -1 19/12.
Simplified, it would be -2 7/12.
