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3 years ago

A triangle has an area of 221.16 in.² the height of the triangle is 29.1 inches what is the length of the base of the triangle

1 answer:

7 0

The formula you should use is Area = 1/2bh, in other words, area equals half times base times height. Now, substitute everything in, the equation should now be 221.16 = 1/2*b*29.1. This simplifies into 221.16 = 14.55b, now divide 14.55 on both sides, which leaves us to 15.2 = b. However, don't forget the units, which the answer (length of base) should be 15.2 in.^2.

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In △ABC, m∠A=57°, m∠B=37°, and a=11. Find c to the nearest tenth.

lilavasa [31]

Answer:

c = 13.1

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

# ∠A is opposite to side a

# ∠B is opposite to side b

# ∠C is opposite to side c

- The sine rule is:

# $\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$

* Lets solve the problem

- In Δ ABC

∵ m∠A = 57°

∵ m∠B = 37°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 57° + 37° + m∠C = 180°

∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides

∴ m∠C = 86°

- Lets use the sine rule to find c

∵ a = 11 and m∠A = 57°

∵ m∠C = 86°

∵ $\frac{sin(57)}{11}=\frac{sin(86)}{c}$

- By using cross multiplication

∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)

∴ $c=\frac{11(sin86)}{sin57}=13.1$

* c = 13.1

4 0

3 years ago

Verify the identity. cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x

DanielleElmas [232]

Cos(x)/(1+sin(x) + (1+sin(x))/cos(x)=

cos²(x)/cos(x)(1+sin(x)) + (1+sin(x))²/cos(x)(1+sin(x))=

cos²(x)+1+2sin(x)+sin²(x) /cos(x)(1+sin(x))=

2+2sin(x) / cos(x)(1+sin(x))=

2(1+sin(x)) / cos(x)(1+sin(x))=

2/cos(x)=

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3 years ago

Given the following perfect square trinomial, fill in the missing term. (2 points) 4x2 + 16x + _____

alukav5142 [94]

4x2+16x+ use the term b

7 0

3 years ago

A concert organizer anticipates selling 4,000 tickets and that a quarter of these will be sold at 20% reduction of original pric

Deffense [45]

Answer:

$ 15.79

Step-by-step explanation:

Let x be the price of full ticket,

∵ Total number of tickets = 4000,

Quarter of 4000 tickets = $\frac{4000}{4}$ = 1000,

Remaining tickets = 4000 - 1000 = 3000,

Since, if the price of each ticket is reduced by 20%,

Then the new price of each ticket = (100 - 20)% of x

= 80% of x

= 0.80x,

According to the question,

The total price of quarters of ticket + total price of remaining tickets = $ 60000

= 0.80x × 1000 + x × 3000 = 60,000

800x + 3000x = 60,000

3800x = 60,000

⇒ x ≈ 15.79

Hence, the price of full ticket is approximately $ 15.79.

7 0

3 years ago

In a right triangle the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg, if c=6, a=

irakobra [83]

Answer:

Step-by-step explanation:

6^2=5^2+b^2

36=25+b

36-25=b

B= square root of 9

B= 3

5 0

3 years ago

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