Steeple

We see the church tower from the road at an angle of 52°. When we zoom out to 29 meters away, it can be seen at an angle of 21°. How high is it?

Correct answer:

h =  15.9 m

Step-by-step explanation:

n=29 m α=52 ° β=21 °  tanα=h/x tanβ=h/(x+n)  x=h/tanα=h t1 t1=1/tanα°=1/tan52° =1/1.279942=0.78129 t2=tanβ°=tan21° =0.383864=0.38386  t2 (h t1+n)=h t2 h t1+n t2=h  h=n t21t2 t1=29 0.383910.3839 0.781315.9008 m   Verifying Solution:  x=h t1=15.9008 0.781312.4231 m T1=x/h=12.4231/15.90080.7813 T2=hx+n=15.900812.4231+290.3839



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