Answer:
The measure of side AB is 6√3 cm.
Step-by-step explanation:
The question is:
In the right triangle shown, ∠A = 30° and BC = 6. What is AB?
Solution:
Consider the right-angled triangle ABC below.
In the triangle:
∠A = 30°
∠B = 90°
BC = 6 cm
According to the trigonometric identities for a right-angled triangle the tangent of an angle is the ratio of the length of perpendicular side to the length of the base.
That is for angle θ° the value of tan θ° is:
![tan\ \theta^{\text{o}}=\frac{Perpendicular}{Base}](https://tex.z-dn.net/?f=tan%5C%20%5Ctheta%5E%7B%5Ctext%7Bo%7D%7D%3D%5Cfrac%7BPerpendicular%7D%7BBase%7D)
In the triangle ABC, the perpendicular side is side BC and the base is AB.
Compute the length of side AB as follows:
![tan\ 30^{\text{o}}=\frac{BC}{AB}](https://tex.z-dn.net/?f=tan%5C%2030%5E%7B%5Ctext%7Bo%7D%7D%3D%5Cfrac%7BBC%7D%7BAB%7D)
The value of tan 30° is,
![tan\ 30^{\text{o}}=\frac{1}{\sqrt{3}}](https://tex.z-dn.net/?f=tan%5C%2030%5E%7B%5Ctext%7Bo%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D)
The value of side AB is:
![tan\ 30^{\text{o}}=\frac{BC}{AB}](https://tex.z-dn.net/?f=tan%5C%2030%5E%7B%5Ctext%7Bo%7D%7D%3D%5Cfrac%7BBC%7D%7BAB%7D)
![\frac{1}{\sqrt{3}}=\frac{6}{AB}\\\\AB=6\times \sqrt{3}\\AB=6\sqrt{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%3D%5Cfrac%7B6%7D%7BAB%7D%5C%5C%5C%5CAB%3D6%5Ctimes%20%5Csqrt%7B3%7D%5C%5CAB%3D6%5Csqrt%7B3%7D)
Thus, the measure of side AB is 6√3 cm.
Answer:
Step-by-step explanation:
We need a system of equations to solve for this. The first equation comes from "The difference between 2 numbers is 12". Difference means subtraction, the 2 numbers will be x and y, and the word "is" means equals:
x - y = 12
The second equation comes from "...their sum is 26". The numbers are still x and y but this time we have their sum, which is what they equal when they are added together. The word "is" means equals:
x + y = 26. So we will go back up to the first equation. If y taken away from x leaves a positive number, that means that y is smaller than x. We are looking for the value of the smaller number so we will find y. Solve the first equation for x to get it in terms of y:
x = 12 + y and we sub that into the second equation:
(12 + y) + y = 26 and
12 + 2y = 26 and
2y = 14 so
y = 7. Choice B is the one you want.
Between 25 through 30 years
Answer:
284.52
Step-by-step explanation:
total area = area of semi circle + area of rectangle
area of semicircle = pi r^2 /2.
= 3.14 * (12/2) ^2 ...divided by 2
= 56.52
area of rectangle = length * breadth
= 19*12
= 228