Answer:
-¹²/₅
Step-by-step explanation:
Let cos a = -⁵/₁₃
Then tan a = sin a/cos a
= [√(1 - cos²a)]/cos a
= {√[1 - (-⁵/₁₃)²]}/(-⁵/₁₃)
= -[√(1 - ²⁵/₁₆₉)] × ¹³/₅
= -[(√(¹⁴⁴/₁₆₉ )] × ¹³/₅
= -¹²/₁₃ × ¹³/₅
= -¹²/₅
tan(arccos (-⁵/₁₃)) = -¹²/₅
The diagram shows the 2nd quadrant of a circle with radius 13, cos a = -⁵/₁₃, and tan a = ¹²/₍₋₅₎ = -¹²/₅.
Answer:
Leon is correct. (Option 1)
Step-by-step explanation:
Given that Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure.
Step 1: Find the greatest common factor of the given lengths: 7
Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5
Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.
we have to explain whether or not Leon is correct.
As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem
⇒
Let a, b, c forms a Pythagorean triplet
Multiplied by 4 on both sides
⇒
⇒
Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.
∴ multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple.
Hence, Leon is correct.