Question

Find the value of
tan 60°
tan 45​

Answer 1

ANSWER:

The values are:

tan(60)= √3

tan (45) = 1

Answer 2

Tan 60°

Consider an equilateral ΔPQR. Since each angle in an equilateral triangle.

∴∠P = ∠Q = ∠R = 60°

Draw a perpendicular PS from P to QR.

Now, In ΔPQS and ΔPRS

• → ∠PSQ=∠PSR [each of 90° ]
• → ∠PQS=∠PRS [each of 60° ]
• → PS=PS [common]

∴ ΔPQS ≅ ΔPRS (A.S.A.congruancy)

→ Let sides PQ = QR = RP = 2x

→ Then, QS = SR= QR/2 = 2x/2 = x

Now, In ΔPSQ

PQ² = QS² +SP² [By Pythagoras theorem]

• → (2x)²= x² +PS²

• → PS² = 3x²

• → PS = √3x

Now, In ΔPSQ

• → tanQ = PS/QS
• → tan60° = √3x/x
• → tan60° = √3

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Tan45°

Let ABC be a right angled isosceles triangle with right angle at A and vertices marked in clockwise direction.

Tangent of any angle in a right angled triangle is the ratio of its opposite side and adjacent side other than the diagonal

Hence ,

• tan∠ABC = tan45° = AC/AB

• As it is an isosceles triangle AC = AB

⇒tan45° = 1