In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.
2 answers:
Answer:
Hypotenuse = 14in
Adjacent = 12.12in
Step-by-step explanation:
Check attachment for diagram
Using SOH, CAH TOA method
According to SOH
Sin(theta) = Opposite/Hypotenuse
Given theta = 30°
Opposite = 7in
Sin30° = 7/Hypotenuse
Hypotenuse = 7/sin30°
Hypotenuse = 7/0.5
Hypotenuse = 14in
The other leg will be the adjacent say x
Using Pythagoras theorem to get x
Hyp² = Opp²+Adj²
14² = 7²+x²
x² = 14²-7²
x² = 196-49
x² = 147
x = √147
x = 12.12in
The value of the other leg is 12.12
You might be interested in
Well, you could assign a letter to each piece of luggage like so...
A, B, C, D, E, F, G
What you could then do is set it against a table (a configuration table to be precise) with the same letters, and repeat the process again. If the order of these pieces of luggage also has to be taken into account, you'll end up with more configurations.
My answer and workings are below...
35 arrangements without order taken into consideration, because there are 35 ways in which to select 3 objects from the 7 objects.
210 arrangements (35 x 6) when order is taken into consideration.
*There are 6 ways to configure 3 letters.
Alternative way to solve the problem...
Produce Pascal's triangle. If you want to know how many ways in which you can choose 3 objects from 7, select (7 3) in Pascal's triangle which is equal to 35. Now, there are 6 ways in which to configure 3 objects if you are concerned about order.
A, B, C, D, E, F, G
What you could then do is set it against a table (a configuration table to be precise) with the same letters, and repeat the process again. If the order of these pieces of luggage also has to be taken into account, you'll end up with more configurations.
My answer and workings are below...
35 arrangements without order taken into consideration, because there are 35 ways in which to select 3 objects from the 7 objects.
210 arrangements (35 x 6) when order is taken into consideration.
*There are 6 ways to configure 3 letters.
Alternative way to solve the problem...
Produce Pascal's triangle. If you want to know how many ways in which you can choose 3 objects from 7, select (7 3) in Pascal's triangle which is equal to 35. Now, there are 6 ways in which to configure 3 objects if you are concerned about order.