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3 years ago

5

Tara wants to fix the location of a mountain by taking measurements from two positions 3 miles apart. From the first position, t

he angle between the mountain and the second position is 78∘. From the second position, the angle between the mountain and the first position is 53∘. Find the distance from each of the positions to the mountain. Round your answers to the nearest tenth of a mile.

1 answer:

Tomtit [17]3 years ago

8 0

Answer:

3.78=156-53=142

answer 142

Step-by-step explanation:

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Hijg is a rectangle. Why is triangle hgi congruent to triangle jig ? Explain your reasoning.

yanalaym [24]

HGI is congruent to JIG due to the Side-Side-Side congruence theorem.

This theorem states that if the three sides of one triangle are congruent to the three sides of another triangle, the triangles must be congruent.

In order to create these triangles, we must draw a diagonal in this triangle. This will be a shared side between both triangles.

A rectangle's opposite sides are congruent; this means the top and left sides, which are part of one triangle, will be congruent to the bottom and right sides, which are part of the other triangle.

This gives us all 3 sides of both triangles congruent, and therefore the congruence theorem applies.

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4 years ago

Read 2 more answers

The base of an isosceles triangle is one and a half times the length of the other two sides.A smaller triangle has a perimeter t

Anna11 [10]

Answer:

Perimeter of the smaller triangle = 1.75x

Step-by-step explanation:

Let the two equal sides of an isosceles triangle = x

Therefore, length of the base = $(1\frac{1}{2})x$

Perimeter of this isosceles triangle = x + x + $(1\frac{1}{2})x$

= 2x + $(1+\frac{1}{2})x$

= 2x + x + $\frac{x}{2}$

= $\frac{5x}{2}$

Since, smaller triangle has a perimeter that is half the perimeter of the larger triangle,

Length of each corresponding side of smaller triangle will be half of the larger triangle.

Length of sides of the smaller triangle = $\frac{x}{2},\frac{x}{2},(1\frac{1}{2})\frac{x}{2}$

Perimeter of the smaller triangle = $\frac{x}{2}+\frac{x}{2}+(1\frac{1}{2})\frac{x}{2}$

= x + $\frac{x}{2}+\frac{x}{4}$

= $\frac{3}{2}x+\frac{x}{4}$

= $\frac{6}{4}x+\frac{x}{4}$

= $\frac{7}{4}x$

= 1.75x

Therefore, expression that represents the perimeter of the smaller triangle is (1.75x)

4 0

3 years ago

Here is some information about 26 houses.a,b and c are all different numbers.Number of bedrooms:1,2,3,4,5.Number of houses:7,a,b

kkurt [141]

Answer:

$[a,b,c]=[4,2,5]$ or $[a,b,c]=[2,4,5]$

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Bedroom} & {1} & {2} & {3} & {4} & {5} \ \\ {Houses} & {7} & {a} & {b} & {c} & {8} \ \end{array}$

$n = 26$

$Median = 3.5$

Required

Find a, b and c

Median is calculated as:

$Median = \frac{n+1}{2}$

$Median = \frac{26+1}{2}$

$Median = \frac{27}{2}$

$Median = 13.5th$

This means that the median is the average of the 13th and 14th item.

$\begin{array}{cccccc}{Bedroom} & {1} & {2} & {3} & {4} & {5} \ \\ {Houses} & {7} & {a} & {b} & {c} & {8} \ \end{array}$

Since the median is $Median = 3.5$ (average of 3 and 4),

and:

$3 \to b \to 13$

$4 \to c \to 14$

This implies that c begins at 14

So, the number of houses bedrooms 4 and 5 is:

$c + 8 = 26 - 14 +1$

$c + 8 = 13$

$c = 5$

Also

$7 + a + b + c + 8 = 26$ ---- sum of total frequency

$a + b + c = 26 - 7 - 8$

$a + b + c = 11$

Substitute $c = 5$

$a + b + 5 = 11$

$a + b = 11 - 5$

$a + b = 6$

Since a, b and c are different, then

a and b cannot be 5 because $c = 5$

a and b cannot be 3 because $a = b =3$

$b \ne 0$ because b ends at 13

a

So, possible sets are:

$[a,b]=[2,4]$

$[a,b]=[4,2]$

Include c, we have:

$[a,b,c]=[4,2,5]$ or $[a,b,c]=[2,4,5]$

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3 years ago

Louise has only 5 cent, 10 cent, and 20 cent coins in her purse. She has 30 coins in total, and she has two more 10 cent coins t

Hoochie [10]

Let x = number of 5 cent coins.
Then there are (x+2) 10 cent coins.
Let y = 20 cent coins.
Total coins: x+(x+2)+y = 30
2x+y=28
y = 28-2x (1)
Total value: 0.05x + 0.1(x+2) + 0.2y = 3.80
0.15x + 0.2y + 0.2 = 3.80
0.15x + 0.2y = 3.60 (2)
Substitute (1) into (2).
0.15x + 0.2(28-2x) = 3.60
-0.25x + 5.60 = 3.60
2.00 = 0.25x
8 = x

From (1), obtain y = 28 - 2(8) = 12
Answer: (x+2) = 8+2 = 10
Louise has 10 10-cent coins

3 0

3 years ago

What is the distance across the river?

elena55 [62]

Answer:

The correct answer is,

d = 300 feet

Step-by-step explanation:

<u>Points to remember </u>

The ratio of of corresponding sides of similar triangles are equal.

From the figure we can see two similar triangles.

<u>To find the value of d</u>

It is given that, the ratio of d to 150 ft is the same as the ratio of 40 ft to 20 ft

d/150 = 40/20

d = (150 * 40)/20

d = 300

Therefore the value of d = 300 ft

8 0

3 years ago