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son4ous [18]
3 years ago
9

In triangle abc, ac=10, bc=8, angle b =90 degrees and angle bda = 90. how long is line bd

Mathematics
1 answer:
WITCHER [35]3 years ago
4 0
The complete question in the attached figure

we know that
<span>applying the Pythagorean theorem in triangle ABC
</span>AC²=AB²+BC²----------> AB²=AC²-BC²---------> 10²-8²-------> AB²=36-----> AB=6

in the triangle ABC
tan a=BC/AB--------> 8/6--------> tan a=4/3
tan c=AB/BC--------> 6/8--------> tan c=3/4

in the triangle ABD
tan a=BD/AD---------> tan a=BD/x-------> BD=x*tan a
BD=x*(4/3)-----------> equation 1

in the triangle BDC
tan c=BD/DC------------------> BD=(10-x)*tan c------> BD=(10-x)*(3/4)
BD=(10-x)*(3/4)-------------> equation 2

equal 1 and 2
x*(4/3)=(10-x)*(3/4)------> 16x=9*(10-x)--------> 16x=90-9x----> 25x=90
x=90/25-----------> x=3.6
BD=x*(4/3)--------> BD=3.6*(4/3)---------->  BD=4.8 units

the answer is BD=4.8 units


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3 years ago
Construct the exponential function that contains the points (0,2) and (3,54)
erma4kov [3.2K]

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

<h3>How to construct the exponential function?</h3>

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

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Take the cube roots of both sides

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So, we have:

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Read more about exponential functions at:

brainly.com/question/24077767

8 0
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Step-by-step explanation:

This should be the answer good luck :)

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