Is the orthocenter of a triangle on the inside ?

Mathematics

2 answers:

Olegator [25]3 years ago

8 0

It isn’t always in the triangle

likoan [24]3 years ago

7 0

Answer:

It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. To make this happen the altitude lines have to be extended so they cross.

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almond37 [142]

Answer: 742

<u>Step-by-step explanation:</u>

The given sequence {27, 31, 35, ... } provides the following information:

the first term (a₁) = 27
the difference (d) = 4

We can use the information above to find the explicit rule of the sequence:

$a_n=a_1+d(n-1)\\.\quad =27+4(n-1)\\.\quad =27+4n-4\\.\quad =23+4n$

We can use the explicit rule to find the 14th term (a₁₄)

$a_n=23+4n\\a_{14}=23+4(14)\\.\quad =23+56\\.\quad =79$

Next, we can input the first and last term of the sequence into the Sum formula:

$S_n=\dfrac{a_1+a_n}{2}\times n\\\\S_{14}=\dfrac{a_1+a_{14}}{2}\times 14\\\\.\quad =\dfrac{27+79}{2}\times 14\\\\.\quad =\dfrac{106}{2}\times 14\\\\.\quad =53\times 14\\\\.\quad =742$