Class 10 Math All topics Some Applications of Trigonometry

One skyscraper is $100dm$. At some time the shadow of a $1dm$ high pole is $33 dm$ long from the light of the sun. What will be the angle of elevation of sun and the length of the shadow and the shadow of the skyscraper at the same time.

Solution: Let $BC$ is a skyscraper of height $100dm$. and $DE$ is a pole of height $9dm$.

Let elevation angle of sun is $θ$.

According to question, $∠DAE=∠CAB=θ$ and $AE=33 dm$

From right angled $ΔDEA$

$tanθ=AEDE $

$=33 9 $

$=3 $

$=tan60_{0}=θ=60_{0}$

Hence, angle of elevation of sun $=60_{0}$

Again from right angled $ΔABC$,

$tanθ=ABBC $

$tan60_{0}=AB100 $

$3 =AB100 $

$AB=3 100 $

Hence, angle of elevation of sun is $60_{0}$ and length of shadow of skyscraper $3 100 $ decimeter.

Let elevation angle of sun is $θ$.

According to question, $∠DAE=∠CAB=θ$ and $AE=33 dm$

From right angled $ΔDEA$

$tanθ=AEDE $

$=33 9 $

$=3 $

$=tan60_{0}=θ=60_{0}$

Hence, angle of elevation of sun $=60_{0}$

Again from right angled $ΔABC$,

$tanθ=ABBC $

$tan60_{0}=AB100 $

$3 =AB100 $

$AB=3 100 $

Hence, angle of elevation of sun is $60_{0}$ and length of shadow of skyscraper $3 100 $ decimeter.

Similar topics

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

surface areas and volumes

introduction to trigonometry

functions

some applications of trigonometry

quadratic equations

surface areas and volumes

Related Questions

Related Questions