Answer:
AC
Step-by-step explanation:
First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:
60 + 3x - 2 + 2x + 7 = 180
5x + 65 = 180
5x = 115
x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.
Answer:

Step-by-step explanation:
Pythagoras theorem states that <em>“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”</em>.

So,
Length of leg y of the right triangle = 13
Answer:
The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0
Step-by-step explanation:
Given Trigonometrical function as :
= 2 (1 + cosec A)
Or,
= 2 (1 + cosec A)
,<u> Now, rationalizing </u>
= 2 (1 + cosec A)
Or,
= 2 ( 1 + 
Or,
= 2 ( 
Or,
= 2 ( 
Or,
= 2 ( 
Or,
= 2 ( 
Or,
= 2 ( 
Or,
= 2 ( 
Or,
= 2 ( 
Or,
= 2 ( 
Or, sin A + sin² A = 2 cos A (1 + sin A)
Or, sin A + sin² A = 2 cos A + 2 cos A × sin A
Or, sin² A + sin A - 2 cos A - 2 cos A × sin A = 0
So,The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0 Answer
Answer:
390cm³
Step-by-step explanation:
IF you look at the figure attached, you will see that your figure is made up of 3 rectangular prisms.
All you need to do is solve for the volume of each prism and add them up together.
The formula to use to get the volume of a rectangular prism is:

Where:
V = Volume
w = width
l = length
h = height
Let's get the first one and double it because you have rectangular prisms with the same dimensions:

Next we get the rectangular prism in the middle:
Notice that the height of the side rectangular prisms is 12 cm. To get the height of the middle figure, just subtract 5cm and 2 cm from the height because they are the excess of the middle.
12cm - (5cm + 2cm)
12 cm - 7cm = 5cm
Then we plug it into the formula

Now that we have the volumes of all figures, just add them up together:
150cm³ + 240cm³ = 390cm³