A ladder is placed against a wall such that the top is 8 feet above the ground. If the ladder is 10 feet long, how far away from
1 answer:
Answer:
6 feet
Step-by-step explanation:
Consider the right triangle formed by the wall, ladder and ground.
Let the distance the ladder is from the wall be d , then
Using Pythagoras' identity in the right triangle
The square on the hypotenuse ( ladder) is equal to the sum of the squares on the other 2 sides ( wall and d ), then
d² + 8² = 10²
d² + 64 = 100 ( subtract 64 from both sides )
d² = 36 ( take the square root of both sides )
d = = 6
That is the ladder is 6 feet away from the wall
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Answer:
a = 7.2
Step-by-step explanation:
The figure has been re-labelled and attached to this response.
From the figure, the larger right triangle DAB and the small right triangle BCA are similar. This is because;
i. They have two corresponding congruent angles which are<em> the right angle</em>
and <em>angle B</em>
Therefore, we can say that;
<em>Cross multiply</em>
a x a = 13 x 4
a² = 52
a = √52
a = 7.2
Note: The figure showing the similar triangles has also been attached to this response.
Answer:
Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.
Step-by-step explanation:
Two quantities P and Q are said to be in PROPORTION if and only if for all values of P and q, we get:
Here, k : PROPORTIONALITY CONSTANT
Case: 1
5 hour piano practice in 1 week.
So, the piano practice in 2 weeks( 1 x 2) = 2 x 5 = 10 hours
But here, it is given to be 12 hours in 2 weeks.
Hence, NOT PROPORTIONAL.
Case 2:
70 words in 60 seconds.
So, the words typed in 210 seconds ( 60 x 3.5) = 70 x 3.5 = 240 words
But here, it is given to be 280 words in 210 seconds.
Hence, NOT PROPORTIONAL.
Case: 3
8 hour homework in 1 week.
So, the homework done in 2 weeks( 1 x 2) = 2 x 8 = 16 hours
It is given to be 16 hours in 2 weeks.
Hence, PROPORTIONAL.
Case: 4
15 miles in 78 minutes.
So, the distance covered in 102 minutes (78 x 1.3) = 15 x 1.3 = 19.6 miles
But here, it is given to be 17 miles in 102 minutes.
Hence, NOT PROPORTIONAL.
Case: 5
18 miles in 45 minutes.
So, the distance covered in 55 minutes (45 x 1.2) = 18 x 1.2 = 21.6 miles
But here, it is given to be 22 miles in 55 minutes.
Hence, NOT PROPORTIONAL.
Hence, the only proportional case is Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.