Answer:
DA = 285.7 m
Step-by-step explanation:
First we need to find the side AB in the triangle ABC, and we can do this using Pythagoras' theorem:
AB^2 = BC^2 + AC^2
AB^2 = 300^2 + 400^2
AB^2 = 25000
AB = 500 m
We can find the angle ABC with the tangent relation:
tangent(ABC) = 400/300 = 4/3
ABC = 53.13°
From triangle ABC, we have:
ABC + BCA + CAB = 180°
53.13 + 90 + CAB = 180
CAB = 36.87°
From triangle DAC, we have:
DAC + ACD + CDA = 180
36.87 + 45 + CDA = 180
CDA = 98.13°
Now to find the side of DA, we can use law of sines in triangle DAC:
DA/sin(DCA) = AC/sin(CDA)
DA/sin(45) = 400/sin(98.13)
DA = 400 * 0.7071 / 0.9899 = 285.7258 m
Rounding to nearest tenth, we have DA = 285.7 m
Answer:
24/25
Step-by-step explanation:
0.96%
96/100
24/25
Option D: 21 in is the base length of the triangular base.
Explanation:
Given that a triangular pyramid with a height of 9 inches has a volume of 63 cubic inches.
The height of the triangular base is 6 inches.
We need to determine the base length of the triangular pyramid.
The base length of the triangular pyramid can be determined using the formula,
Substituting 
and 
in the above formula, we get,
Simplifying the terms, we get,
Dividing both sides by 3, we have,
Thus, the base length of the triangular pyramid is 21 in
Hence, Option D is the correct answer.
Dilation involves changing the size of a shape
<h3>How to determine the relationship between the trigonometry ratios</h3>
From the question, we understand that:
The dilation of triangle XYZ gives triangle ACB
This means that, the following are corresponding points
- Points X and A
- Points Y and C
- Points Z and B
The above means that:
The relationships between the trigonometry ratios of both triangles are:
cos(X) = cos(A), cos(Y) = cos(C) and cos(Z) = cos(B)
<h3>How to determine the measures of segments AC and AB</h3>
In (a), segments XY and XZ corresponds to the segments AC and AB
So, the product of the lengths of XY and XZ and the scale factor will result in the lengths of AC and AB,
i.e.
AC = 2 * XY and AB = 2 * XZ
Read more about dilation at:
brainly.com/question/26332230
This is = 4 therefore no property is applied
