All categories

3 years ago

The acute angles of a right triangle are in the ratio of 7:11. Find the measure of each angle.

Mathematics

2 answers:

kondor19780726 [428]3 years ago

4 0

Answer:

Step-by-step explanation:

Since it's a right angle triangle, one angle has to be 90.

Total angle in a triangle = 180

Other two should add up to 90.

7/18 × 90 = 35

11/18 × 90 = 55

Tbe angles are 35°, 55° and 90°

nalin [4]3 years ago

4 0

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Therefore measures of acute angles will be 7x and 11x.

$\therefore \: 90 \degree + 7x + 11x = 180 \degree \\ \\ \therefore \: 18x = 180 \degree - 90 \degree \\ \\ \therefore \: 18x = 90 \degree \\ \\ \therefore \: x = \frac{90 \degree }{18} \\ \\ \therefore \: x = 5\degree \\ \\ \therefore \: 7x = 7 \times 5\degree = 35\degree \\ \& \: 11x = 11 \times 5\degree = 55\degree$

Hence, measure of each angle of right triangle are 35°, 55°, 90°.

Thus, option B is the correct answer.

You might be interested in

Distributive property equations are equations when you are ____ one term with another 2 or more terms inside parentheses.

Mariulka [41]

I think the answer is multiplying

5 0

2 years ago

On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees

Ann [662]

Answer:

59.87% probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent

Step-by-step explanation:

For each employee, there are only two possible outcomes. Either they are absent, or they are not. The probability of an employee being absent is independent from other employees. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5% of the production employees at Midland States Steel are absent from work.

This means that $p = 0.05$

What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent

This is P(X = 0) when n = 10. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.05)^{0}.(0.95)^{10} = 0.5987$

59.87% probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent

4 0

3 years ago

Select the correct answer.

borishaifa [10]

The answer should be B

5 0

3 years ago

const2013 [10]

Answer:

the third

Step-by-step explanation:

your photo is not clear, and your explanations for your question is not clear also.

as we are tackling the substraction and the addition questions between matricxs.We could simply +/- every number correspondingly.

4 0

3 years ago

A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

3 years ago