Find the measure of each indicated angle

A 32 foot ladder is leaning against a building and forms a 29.37 angle with the ground how far away from the building is the bas

BARSIC [14]

Answer:

the base of the ladder is 27.89 ft away from the building

Step-by-step explanation:

Notice that this situation can be represented with a right angle triangle. The right angle being that made between the ground and the building, the ladder (32 ft long) being the hypotenuse of the triangle, the acute angle of $29.37^o$ being adjacent to the unknown side we are asked about (x). So, we can use the cosine function to solve this:

$cos(\theta)=\frac{adjacent}{hypotenuse} \\cos(29.37^o)=\frac{x}{32\,\,ft}\\32 \,\,cos(29.37^o)\,\,ft=x\\x=27.887\,\,ft$

which rounded to the nearest hundredth gives;

x = 27.89 ft

6 0

2 years ago

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The vertices of ΔRST are R(–1,–1), S(–1,11) and T(4,11). Which could be the side lengths of a triangle that is similar but not c

Step2247 [10]

The side lengths could be 10, 24 and 26 units.

We must first find the side lengths. We use the distance formula to do this.

For RT:
$d=\sqrt{(11--1)^2+(-1--1)^2}
\\=\sqrt{(11+1)^2+(-1+1)^2}
\\=\sqrt{12^2+0^2}=\sqrt{144}=12$

For ST:
$d=\sqrt{(11-11)^2+(4--1)^2}
\\=\sqrt{0^2+(4+1)^2}=\sqrt{5^2}=\sqrt{25}=5$

For TR:
$d=\sqrt{(11--1)^2+(4--1)^2}
\\=\sqrt{(11+1)^2+(4+1)^2}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$

Our side lengths, from least to greatest, are 5, 12 and 13.

To be similar but not congruent, the side lengths must have the same ratio between corresponding sides but not be the same length. 10, 24 and 26 are all 2x the original side lengths, so this works.

5 0

2 years ago

The US Department of Health and Human Services wants to know whether the national healthcare system is achieving its goals in Vi

Vlad [161]

Answer:

Part. B

bc it was 71%

6 0

2 years ago

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a school baseball team raised $810 for new uniforms. each player on the team sold one book of tickets. There were 10 tickets in

antiseptic1488 [7]

27
Multiply 10 and 3 because thats how much each book is worth.
Then divide 810 by 30
The answer is 27

6 0

2 years ago

Leah borrows £10,000 over 5 years at a simple interest rate of 15%.

Fynjy0 [20]

Answer:

She will pay $7,500 interest over the 5 years

She will have to pay back $17,500 in total

Step-by-step explanation:

Let us revise the rule of the simple interest

I = Prt and A = P(1 + rt) , where:

A = Total Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Rate of Interest per year in decimal

t = Time Period involved in months or years

∵ Leah borrows £10,000 over 5 years at a simple interest rate of 15%.

∴ P = 10,000

∴ t = 5

∴ r = 15% = $\frac{15}{100}$ = 0.15

→ Substitute them in the first rule to find the interest

∵ I = 10,000(0.15)(5)

∴ I = 7,500

∴ She will pay $7,500 interest over the 5 years

→ Let us find A

∵ A = 10,000(1 + 0.15×5)

∴ A = 17,500

∴ She will have to pay back $17,500 in total

5 0

2 years ago