Answer:
2(2x+5)
Step-by-step explanation:
Length of the rectangle=l= 3x
Breadth of the rectangle=b= 5
Perimeter= 2(l+b)
= 2(3x+5)
Answer:
-7j-k-1
Step-by-step explanation:
1)
∠BAC = ∠NAC - ∠NAB = 144 - 68 = 76⁰
AB = 370 m
AC = 510 m
To find BC we can use cosine law.
a² = b² + c² -2bc*cos A
|BC|² = |AC|²+|AB|² - 2|AC|*|AB|*cos(∠BAC)
|BC|² = 510²+370² - 2*510*370*cos(∠76⁰) =
|BC| ≈ 553 m
2)
To find ∠ACB, we are going to use law of sine.
sin(∠BAC)/|BC| = sin(∠ACB)/|AB|
sin(76⁰)/553 m = sin(∠ACB)/370 m
sin(∠ACB)=(370*sin(76⁰))/553 =0.6492
∠ACB = 40.48⁰≈ 40⁰
3)
∠BAC = 76⁰
∠ACB = 40⁰
∠CBA = 180-(76+40) = 64⁰
Bearing C from B =360⁰- 64⁰-(180-68) = 184⁰
4)
Shortest distance from A to BC is height (h) from A to BC.
We know that area of the triangle
A= (1/2)|AB|*|AC|* sin(∠BAC) =(1/2)*370*510*sin(76⁰).
Also, area the same triangle
A= (1/2)|BC|*h = (1/2)*553*h.
So, we can write
(1/2)*370*510*sin(76⁰) =(1/2)*553*h
370*510*sin(76⁰) =553*h
h= 370*510*sin(76⁰) / 553= 331 m
h=331 m
Answer:
Step-by-step explanation:
We can use the Law of Sines to find segment AD, which happens to be a leg of and the hypotenuse of .
The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:
Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:
Now use this value in the Law of Sines to find AD:
Recall that and :
Now that we have the length of AD, we can find the length of AB. The right triangle is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio , where is the side opposite to the 30 degree angle and is the length of the hypotenuse.
Since AD is the hypotenuse, it must represent in this ratio and since AB is the side opposite to the 30 degree angle, it must represent in this ratio (Derive from basic trig for a right triangle and ).
Therefore, AB must be exactly half of AD:
7y +8= 9+3y+2y
Combine like terms.
7y+8= 9+5y
Subtract 5y on both sides.
2y+8=9
Subtract 8 on both sides.
2y=1
Your answer is 2y=1
I hope this helps!
~kaikers