Finding the length of the other leg

Question

Question #1-The hypotenuse of a right triangle is 22 feet, and one of its legs is 17 feet. Find the length of the other leg. Round to the nearest tenth.

 

Question #2- A utility pole 8 meters tall casts a 12- meter shadow. At the same time a building casts a 99-meter shadow. How tall is the building?

 

Question #3- Find the amount of simple interest on an investment of $3,100 for 2 and a half years at an annual rate of 4 and three fourths%. Round to the nearest cent. 

 

Please answer me as soon as possible by today would be great. Thank you so much =)

Answer 1

Hi, Diana,

#1. The Pythagorean theorem tells us that the sum of the squares of the two perpendicular sides of a right triangle is equal to the square of the hypotenuse, or a² + b² = c². In this case, we are given the length of the hypotenuse (c), and the length of one other side (a or b). So:

a² + (17)² = (22)²

Can you rearrange and solve for the final leg, a?

#2. Another right triangle question - in this case, we know that when the vertical side (height of the tree) is 8m, the horizontal side (length of the shadow) is 12m. If we wanted to, we could use these numbers to determine the angle of the sun (because tan(θ)=opp/adj). The problem is asking about another situation at the same time, so the sun is in the same position, so the angle would be the same. Because the angle is the same, the opp/adj ratio would be the same, so we can set up a proportional equation:

  8   =   x   
 12       99

Can you solve for x, the height of the building?

#3. The amount of simple interest paid is equal to the (Principal)*(Interest rate)*(Period invested)

 

In this case, the amount of simple interest would be ($3100)*(4.75/100)*(2.5)

 

I hope this helps!

Answer 2

This is straight forward application of Pythagoras theorem:

1. 

  X - length of the unknown leg:

 

  X =√(22^2-17^2 ) = 14.0

 #2

   8/12 = X /99

   

   2/3 = X/99

 

   2* 99 = 3X

 

   X = 66

 

#3

 3100 * 0.0475 * 2.5 = 368.13