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3 years ago

Find the area of a triangle with sides of length 6 and 7 and included angle 74°. (round your answer to one decimal place.)

1 answer:

5 0

We use this formula:
Area = ½ • side 1 • sine (A) • side 2
Area = ½ • 6 • sine (74) • 7
Area = 21 • sine (74)
Area = 21*0.96126
Area = 20.18646 
Area = 20.2 (rounded)
Source:
http://www.1728.org/triang.htm

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Where is a major league ballpark in which the distance from home plate to the center-field fence and the height of the center fi

jonny [76]

Given:

A height of 2 feet above the ground and angle of elevation of 86 degrees.

Assuming that the form of our problem is a right triangle, we can solve for the remaining angle:

180 - (90+86) = 4 degrees

The distance from the home plate to the centerfield is

2/sin 4 = x / sin 86

solve for x

x = 28.60 feet

8 0

3 years ago

Find the slope of the line that contains the points (6, -2) and (-3, 7).

Ira Lisetskai [31]

Slope = (y2 - y1)/(x2 - x1)
slope = (7 - -2)/(-3 - 6)
slope = 9/-9
slope = -1

4 0

3 years ago

Find the measure of the missing angle.

Nostrana [21]

180 minus 90 equals 90, divided by 2, the answer is 45 degrees

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3 years ago

On a coordinate plane, triangles P Q R and S T U are shown. Triangle P Q R has points (4, 4), (negative 2, 0), (negative 2, 4).

mamaluj [8]

Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.

The distance between two points on the coordinate plane is given as:

$Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6$

In triangle STU:

$|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2$

|QR| / |TU| = 4/2 = 2

|PR| / |SU| = 6/3 = 2

|PQ| / |ST| = 2√13 / √13 = 2

Hence:

|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|

Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.

6 0

3 years ago

Read 2 more answers

3. From 2005 to 2015, a population of lions is modeled by the equation = 1500 · (0. 98)^t where t is the number of years since 2

SVEN [57.7K]

ANSWER and EXPLANATION

The population of lions is modeled by the equation:

$P=1500\cdot(0.98)^t$

where t = number of years since 2005.

(a) To find the number of lions there in 2005, we have to find P when t is 0:

$\begin{gathered} P=1500\cdot(0.98)^0 \\ P=1500\cdot1 \\ P=1500\text{ lions} \end{gathered}$

There were 1500 lions.

(b) The given function is an exponential function. The exponential factor in the function is 0.98.

In an exponential function, when the exponential factor is less than 1, it means that the function is a decay, hence, it is a decreasing function.

Hence, the population of lions was decreasing over the decade.

That is:

$\begin{gathered} P=1500\cdot0.98^{10} \\ P=1500\cdot0.8171 \\ P\approxeq1,226\text{ lions} \end{gathered}$

That is the answer.

5 0

1 year ago