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yan [13]
3 years ago
14

A triangular plot of land has one side along a straight road measuring 294 feet. a second side makes a 63degrees angle with the​

road, and the third side makes a 56degrees angle with the road. how long are the other two​ sides?
Mathematics
1 answer:
creativ13 [48]3 years ago
6 0
The side across from the 63° angle is 299.5 ft and the side across from the 56° angle is 278.7 ft.

We will use the Law of Sines to solve this.  First, the angle across from the 63° angle:
sin 61/294 = sin 63/x

Cross multiply:
x*sin 61 = 294 sin 63

Divide by sin 61:
(x sin 61)/(sin 61) = (294 sin 63)/(sin 61)
x = 299.5

For the side across from the 56° angle:
sin 61/294 = sin 56/x

Cross multiply:
x*sin 61 = 294 sin 56

Divide both sides by sin 61:
(x sin 61)/(sin 61) = (294 sin 56)/(sin 61)
x = 278.7
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a 9ft ladder is placed 4.5 feet from the base of a wall. How high up will the ladder reach? Round to the nearest hundredth.
spin [16.1K]

Answer:

\huge\boxed{7.79 \ \text{feet}}

Step-by-step explanation:

We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.

This can be represented as a triangle, where x is the unknown side.

    |\

    |  \

x   |    \      9

    |      \

    |        \                  

    |_____\

    4.5

We can use The Pythagorean Theorem to find the value of x. The theorem states that a^2+b^2=c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.

However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.

a^2 + 4.5^2 = 9^2\\\\a^2 + 20.25 = 81\\\\a^2 = 60.75\\\\a \approx 7.79

Hope this helped!

7 0
2 years ago
The distance between -2 and 4 on the number line can be found by which expression
Dahasolnce [82]
4 - -2

,...........................
6 0
3 years ago
Read 2 more answers
In 1960, the population of a town was 14 thousand people. Over the course of the next 50 years, the town grew at a rate of 30 pe
andre [41]

SOLUTIONS

Given: Assume y is the population

\begin{gathered} t=0=1960,y=14030 \\ t=1=1961,y=14060 \\ so\text{ b = 14000} \\ so\text{ k = 30} \end{gathered}

The town grow at the rate of 30 people per year.

y=kt+14000y=30t+14000

(A) The population predicted to be in 2030 will be

\begin{gathered} 2030-1960=70 \\ y=30k+14000 \\ y=30(70)+14000 \\ y=2100+14000 \\ y=16100people \end{gathered}

(B) so when y = 15000, find t

\begin{gathered} y=15000 \\ y=30t+14000 \\ 15000=30t+14000 \\ 15000-14000=30t \\ 1000=30t \\ t=\frac{1000}{30} \\ t\approx33 \\ t=1960+33 \\ t=1993 \end{gathered}

3 0
8 months ago
Solve the equation by using square roots. 2 x 2 − 9 = 11
VashaNatasha [74]

Answer:

x = ± \sqrt{10}

Step-by-step explanation:

Given

2x² - 9 = 11 ( add 9 to both sides )

2x² = 20 ( divide both sides by 2 )

x² = 10 ( take the square root of both sides )

x = ± \sqrt{10} ← exact solutions

3 0
2 years ago
Explain please and tell me how to do it ?
SCORPION-xisa [38]

The trick to calculating the area here is to subdivide the diagram into smaller parts. For example, there's a 3 cm-by-3cm square. The rectangle is 4 cm by 8 cm.. The triangle has a base of 5 cm and a height of 3 cm.

Total area = area of square + area of rectangle + area of triangle

= 9 cm^2 + 32 cm^2 + (1/2)(5 cm)(3 cm)

= (9 + 32 + 7.5) cm^2

= 48.5 cm^2 (total area of figure)

8 0
3 years ago
Read 2 more answers
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