Answer:
Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
Step-by-step explanation:
The illustration form a triangle that can be demarcated into 2 right angle triangle. One triangle representing depression triangle and the other elevation triangle.
Depression triangle 
The opposite side of the triangle formed is the length of the pole from the base to the horizontal line of sight. Therefore,
using tangential ratio
tan 35° = opposite/adjacent
tan 35° = a/8
cross multiply
a = 8 tan 35°
a = 8 × 0.70020753821
a = 5.60166030568
a = 5.602 ft
Elevation triangle 
The opposite side of this right angle triangle represent the length from the horizontal line of sight to the top of the lamppost. 
tan 20° = opposite/adjacent
tan 20° = b/8
cross multiply
b = 8 tan 20°
b = 8 × 0.36397023426
b = 2.91176187413
b = 2.912 ft
Height of the lamppost = 5.602 ft + 2.912 ft = 8.514 ft
 
        
             
        
        
        
Answer:
z=-3
Step-by-step explanation:
-5z+9=24 so, subtract 9 from both sides becuase of liked terms to get -5z=15, then divide both sides by -5 to get z = -3 hope it helps:)
 
        
             
        
        
        
Answer: 1 and 13
Step-by-step explanation: To find the factors of 13, begin by dividing 13 by 1 which gives us 13. This tells us that 1 and 13 are factors of 13.
13 is a prime number which means it only has two factors which are 1 and 13. 
 
        
                    
             
        
        
        
Answer:
Step-by-step explanation:
The ratio of corresponding sides DN and KI is 12 : 4 = 3 : 1. The same ratio applies to altitudes DQ and KO. Since the difference between these altitudes is 6 and the difference between their ratio units is 3-1 = 2, each ratio unit must stand for 6/2 = 3 units of linear measure. That is, ...
   DQ = (3 units)·3 = 9 units
   KO = (3 units)·1 = 3 units
Then the base lengths QN and OI can be found from the Pythagorean theorem:
   KI² = KO² +OI²
   4² = 3² +OI²
   OI = √(16 -9)
   OI = √7
   QN = 3·OI = 3√7
 
        
             
        
        
        
Answer: The answer is B 
Step-by-step explanation: I got the answer right