The measures of the angles of a triangle are shown in the figure below. Solve for x.

Mathematics

1 answer:

Stells [14]2 years ago

5 0

Angles will add up to 180.
49+62+x=180
111+x=180
subtract 111 both sides
x= 69°

Hope this helps!

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Find the volume of the solid, please

dsp73

Answer:

$V \approx=1436.8$

Step-by-step explanation:

Variables and symbols:

r = radius
V = volume
A = surface area
C = circumference
π = pi = 3.1415926535898
√ = square root

Volume of a sphere in terms of radius:

$V = \frac{4}{3}\pi r^3$ , $V \approx 4.1888r^3$

To calculate the volume of a sphere:

Usually the hardest part is measuring or estimating the diameter of the sphere. Special tools exist for smaller parts like balls in ball-bearings, but it gets more complicated if the size is large. Knowing that the diameter is the largest internal measurement you can take should help.

Once you have the measurement, to find the volume use the formula above, in which π is the well-known mathematical constant equal to about 3.14159. To adjust for a half-sphere calculation, just divide the result by two.

Spheres and half-spheres are useful in engineering and architecture due to their property of being able to take equal amounts of pressure or force from each direction.

Solution:

$V=\frac{4}{3} \pi r^{3} =\frac{4}{3} *\pi *7^{3} \approx1436.75504$

Round to nearest tenth: $1436.8$

5 0

2 years ago

Read 2 more answers

The sides of a right triangle measure 6 times the square root of 3, 6 inches, and 12 inches. If an altitude is drawn from the ri

VARVARA [1.3K]

Length of segment of the hypotenuse adjacent to the shorter leg is 5 inches and the length of the altitude is 3 inches.

Step-by-step explanation:

Step 1: Let the triangle be ΔABC with right angle at B. The altitude drawn from B intersects the hypotenuse AC at D. So 2 new right angled triangles are formed, ΔADB and ΔCDB.

Step 2: According to a theorem in similarity of triangles, when an altitude is drawn from any angle to the hypotenuse of a right triangle, the 2 newly formed triangles are similar to each other as well as to the bigger right triangle. So ΔABC ~ ΔADB ~ ΔCDB.

Step 3: Identify the corresponding sides and form an equation based on proportion. Let the length of the altitude be x. Considering ΔABC and ΔADB, AB/DB = AC/AB

⇒ 6/x = 12/6

⇒ 6/x = 2

⇒ x = 3 inches

Step 4: To find length of the hypotenuse adjacent to the shorter leg (side AB of 6 inches), consider ΔADB.

⇒ $AD^{2} + BD^{2} = AB^{2}$