You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

In an acute-a...

Question

In an acute-angled triangle $A B C$ , the points $D, E$ and $F$ are the feet of the perpendiculars from $A, B$ and $C$ onto $B C, A C$ and $A B,$ respectively. The point $H$ is the orthocenter. If $sin A = 3 / 5$ and $B C = 39$ then find the length of $A H$

52

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

65

No worries! We‘ve got your back. Try BYJU‘S free classes today!

43

No worries! We‘ve got your back. Try BYJU‘S free classes today!

27

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $52$
Given $sin A = 3 / 5 \Rightarrow cos A = 4 / 5$

Also $a = 39$
$∴ \frac{a}{sin A} = 2 R$
$\frac{39 \times 5}{3} = 2 R$

$2 R = 65$

$\Rightarrow A H = 2 R cos A = 65 \times \frac{4}{5} = 52$

Suggest Corrections

Similar questions

Q. In an acute angled triangle ABC, D,E and F are the feets of perpendiculars from A,B and C respectively and H is the orthocenter.

If sin A = \frac{3}{5} and BC = 39, then length of AH =

Q. Let ABC be an acute angled triangle in which D, E, F are points on BC, CA, AB respectively such that AD

⊥

BC, AE=EC and CF bisects

∠

C internally. Suppose CF meets AB and DE in M and N respectively. If FM

= 2

, MN

= 1

, NC

= 3

, Find the perimeter of the triangle ABC.

Q. Let

A B C

be an acute angled triangle in which

D, E, F

are points on

B C, C A, A B

respectively such that

A D ⊥ B C, A E = E C

and

C F

bisects

∠ C

internally. Suppose

C F

meets

A D

and

D E

M

and

N

respectively. If

F M = 2, M N = 1, N C = 3

. Find the perimeter of the triangle

A B C

Q. In the given figure, triangle

A B C

is right - angled at

B

. Given that

D E = 3 c m

A E = 5 c m

and

D

and

E

are the mid-points of the sides

A B

and

A C

respectively. If

D E ∥ B C

, find the sides

A B

and

B C

In Fig., a circle inscribed in triangle ABC touches its sides AB,BC and AC at points D,E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

Join BYJU'S Learning Program

In an acute-angled triangle ABC, the points D,Eand F are the feet of the perpendiculars from A,B and C onto BC,AC and AB, respectively. The point H is the orthocenter. If sinA=3/5 and BC=39 then find the length of AH

The correct option is A 52Given sinA=3/5⇒cosA=4/5 Also a=39∴asinA=2R39×53=2R 2R=65 ⇒AH=2RcosA=65×45=52

In an acute-angled triangle $A B C$ , the points $D, E$ and $F$ are the feet of the perpendiculars from $A, B$ and $C$ onto $B C, A C$ and $A B,$ respectively. The point $H$ is the orthocenter. If $sin A = 3 / 5$ and $B C = 39$ then find the length of $A H$

The correct option is A $52$
Given $sin A = 3 / 5 \Rightarrow cos A = 4 / 5$

Also $a = 39$
$∴ \frac{a}{sin A} = 2 R$
$\frac{39 \times 5}{3} = 2 R$

$2 R = 65$

$\Rightarrow A H = 2 R cos A = 65 \times \frac{4}{5} = 52$